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Beyond the Hellings-Downs curve: Non-Einsteinian gravitational waves in pulsar timing array correlations (2310.07537v2)

Published 11 Oct 2023 in gr-qc and astro-ph.CO

Abstract: The recent astronomical milestone by the pulsar timing arrays (PTA) has revealed galactic-size gravitational waves (GW) in the form of a stochastic gravitational wave background (SGWB), correlating the radio pulses emitted by millisecond pulsars. This draws the outstanding questions toward the origin and the nature of the SGWB; the latter is synonymous to testing how quadrupolar the inter-pulsar spatial correlation is. In this paper, we tackle the nature of the SGWB by considering correlations beyond the Hellings-Downs (HD) curve of Einstein's general relativity. We put the HD and non-Einsteinian GW correlations under scrutiny with the NANOGrav and the CPTA data, and find that both data sets allow a graviton mass $m_{\rm g} \lesssim 1.04 \times 10{-22} \ {\rm eV}/c2$ and subluminal traveling waves. We discuss gravitational physics scenarios beyond general relativity that could host non-Einsteinian GW correlations in the SGWB and highlight the importance of the cosmic variance inherited from the stochasticity in interpreting PTA observation.

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References (108)
  1. G. Agazie et al. (NANOGrav), “The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background,” Astrophys. J. Lett. 951, L8 (2023a), arXiv:2306.16213 [astro-ph.HE] .
  2. D. J. Reardon et al., “Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array,” Astrophys. J. Lett. 951, L6 (2023), arXiv:2306.16215 [astro-ph.HE] .
  3. J. Antoniadis et al., “The second data release from the European Pulsar Timing Array I. The dataset and timing analysis,”   (2023), 10.1051/0004-6361/202346841, arXiv:2306.16224 [astro-ph.HE] .
  4. H. Xu et al., “Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I,” Res. Astron. Astrophys. 23, 075024 (2023), arXiv:2306.16216 [astro-ph.HE] .
  5. R. Abbott et al. (LIGO Scientific, VIRGO, KAGRA), “GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run,”   (2021), arXiv:2111.03606 [gr-qc] .
  6. J. D. Romano and B. Allen, “Answers to frequently asked questions about the pulsar timing array Hellings and Downs correlation curve,”   (2023), arXiv:2308.05847 [gr-qc] .
  7. S. L. Detweiler, “Pulsar timing measurements and the search for gravitational waves,” Astrophys. J. 234, 1100–1104 (1979).
  8. J. D. Romano and N. J. Cornish, “Detection methods for stochastic gravitational-wave backgrounds: a unified treatment,” Living Rev. Rel. 20, 2 (2017), arXiv:1608.06889 [gr-qc] .
  9. S. Burke-Spolaor et al., ‘‘The Astrophysics of Nanohertz Gravitational Waves,” Astron. Astrophys. Rev. 27, 5 (2019), arXiv:1811.08826 [astro-ph.HE] .
  10. N. S. Pol et al. (NANOGrav), “Astrophysics Milestones for Pulsar Timing Array Gravitational-wave Detection,” Astrophys. J. Lett. 911, L34 (2021), arXiv:2010.11950 [astro-ph.HE] .
  11. R. W. Hellings and G. W. Downs, “Upper limits on the isotropic gravitational radiation background from pulsar timing analysis,” Astrophys. J. Lett. 265, L39–L42 (1983).
  12. F. A. Jenet and J. D. Romano, “Understanding the gravitational-wave Hellings and Downs curve for pulsar timing arrays in terms of sound and electromagnetic waves,” Am. J. Phys. 83, 635 (2015), arXiv:1412.1142 [gr-qc] .
  13. E. S. Phinney, “A Practical theorem on gravitational wave backgrounds,”   (2001), arXiv:astro-ph/0108028 .
  14. G. Hobbs et al., “The international pulsar timing array project: using pulsars as a gravitational wave detector,” Class. Quant. Grav. 27, 084013 (2010), arXiv:0911.5206 [astro-ph.SR] .
  15. K. Lee, F. A. Jenet, R. H. Price, N. Wex,  and M. Kramer, “Detecting massive gravitons using pulsar timing arrays,” Astrophys. J. 722, 1589–1597 (2010), arXiv:1008.2561 [astro-ph.HE] .
  16. K. J. Lee, N. Wex, M. Kramer, B. W. Stappers, C. G. Bassa, G. H. Janssen, R. Karuppusamy,  and R. Smits, “Gravitational wave astronomy of single sources with a pulsar timing array,” Mon. Not. Roy. Astron. Soc. 414, 3251 (2011), arXiv:1103.0115 [astro-ph.HE] .
  17. L. Dai, M. Kamionkowski,  and D. Jeong, “Total Angular Momentum Waves for Scalar, Vector, and Tensor Fields,” Phys. Rev. D 86, 125013 (2012), arXiv:1209.0761 [astro-ph.CO] .
  18. N. Yunes and X. Siemens, “Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar Timing-Arrays,” Living Rev. Rel. 16, 9 (2013), arXiv:1304.3473 [gr-qc] .
  19. S. J. Vigeland and M. Vallisneri, “Bayesian inference for pulsar timing models,” Mon. Not. Roy. Astron. Soc. 440, 1446–1457 (2014), arXiv:1310.2606 [astro-ph.IM] .
  20. A. N. Lommen, “Pulsar timing arrays: the promise of gravitational wave detection,” Rept. Prog. Phys. 78, 124901 (2015).
  21. S. Vagnozzi, “Implications of the NANOGrav results for inflation,” Mon. Not. Roy. Astron. Soc. 502, L11–L15 (2021), arXiv:2009.13432 [astro-ph.CO] .
  22. S. R. Taylor, “The Nanohertz Gravitational Wave Astronomer,”   (2021), arXiv:2105.13270 [astro-ph.HE] .
  23. B. Allen, “Variance of the Hellings-Downs correlation,” Phys. Rev. D 107, 043018 (2023), arXiv:2205.05637 [gr-qc] .
  24. R. C. Bernardo and K.-W. Ng, “Pulsar and cosmic variances of pulsar timing-array correlation measurements of the stochastic gravitational wave background,” JCAP 11, 046 (2022), arXiv:2209.14834 [gr-qc] .
  25. R. C. Bernardo and K.-W. Ng, “Hunting the stochastic gravitational wave background in pulsar timing array cross correlations through theoretical uncertainty,” JCAP (to appear)  (2023a), arXiv:2304.07040 [gr-qc] .
  26. B. Allen and J. D. Romano, “The Hellings and Downs correlation of an arbitrary set of pulsars,”  (2022), arXiv:2208.07230 [gr-qc] .
  27. B. Allen et al., “The International Pulsar Timing Array checklist for the detection of nanohertz gravitational waves,”   (2023), arXiv:2304.04767 [astro-ph.IM] .
  28. P. D. Lasky et al., “Gravitational-wave cosmology across 29 decades in frequency,” Phys. Rev. X 6, 011035 (2016), arXiv:1511.05994 [astro-ph.CO] .
  29. M. Bailes et al., “Gravitational-wave physics and astronomy in the 2020s and 2030s,” Nature Reviews Physics 3, 344–366 (2021).
  30. G. Lambiase, L. Mastrototaro,  and L. Visinelli, “Astrophysical neutrino oscillations after pulsar timing array analyses,”   (2023), arXiv:2306.16977 [astro-ph.HE] .
  31. R. M. Shannon et al., “Gravitational waves from binary supermassive black holes missing in pulsar observations,” Science 349, 1522–1525 (2015), arXiv:1509.07320 [astro-ph.CO] .
  32. C. M. F. Mingarelli et al., “The Local Nanohertz Gravitational-Wave Landscape From Supermassive Black Hole Binaries,” Nature Astron. 1, 886–892 (2017), arXiv:1708.03491 [astro-ph.GA] .
  33. T. Liu and S. J. Vigeland, “Multi-messenger Approaches to Supermassive Black Hole Binary Detection and Parameter Estimation: Implications for Nanohertz Gravitational Wave Searches with Pulsar Timing Arrays,” Astrophys. J. 921, 178 (2021), arXiv:2105.08087 [astro-ph.HE] .
  34. Z. Arzoumanian et al. (NANOGrav), “The NANOGrav 12.5-year Data Set: Search for Non-Einsteinian Polarization Modes in the Gravitational-wave Background,” Astrophys. J. Lett. 923, L22 (2021a), arXiv:2109.14706 [gr-qc] .
  35. G. Agazie et al. (NANOGrav), “The NANOGrav 15 yr Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries,” Astrophys. J. Lett. 951, L50 (2023b), arXiv:2306.16222 [astro-ph.HE] .
  36. J. Ellis, M. Fairbairn, G. Hütsi, J. Raidal, J. Urrutia, V. Vaskonen,  and H. Veermäe, “Gravitational Waves from SMBH Binaries in Light of the NANOGrav 15-Year Data,”   (2023a), arXiv:2306.17021 [astro-ph.CO] .
  37. Z.-C. Chen, C. Yuan,  and Q.-G. Huang, “Pulsar Timing Array Constraints on Primordial Black Holes with NANOGrav 11-Year Dataset,” Phys. Rev. Lett. 124, 251101 (2020), arXiv:1910.12239 [astro-ph.CO] .
  38. Z. Arzoumanian et al. (NANOGrav), “Searching for Gravitational Waves from Cosmological Phase Transitions with the NANOGrav 12.5-Year Dataset,” Phys. Rev. Lett. 127, 251302 (2021b), arXiv:2104.13930 [astro-ph.CO] .
  39. X. Xue et al., “Constraining Cosmological Phase Transitions with the Parkes Pulsar Timing Array,” Phys. Rev. Lett. 127, 251303 (2021), arXiv:2110.03096 [astro-ph.CO] .
  40. C. J. Moore and A. Vecchio, “Ultra-low-frequency gravitational waves from cosmological and astrophysical processes,” Nature Astron. 5, 1268–1274 (2021), arXiv:2104.15130 [astro-ph.CO] .
  41. A. Afzal et al. (NANOGrav), “The NANOGrav 15 yr Data Set: Search for Signals from New Physics,” Astrophys. J. Lett. 951, L11 (2023), arXiv:2306.16219 [astro-ph.HE] .
  42. S. Vagnozzi, “Inflationary interpretation of the stochastic gravitational wave background signal detected by pulsar timing array experiments,” JHEAp 39, 81–98 (2023), arXiv:2306.16912 [astro-ph.CO] .
  43. G. Franciolini, D. Racco,  and F. Rompineve, “Footprints of the QCD Crossover on Cosmological Gravitational Waves at Pulsar Timing Arrays,”   (2023), arXiv:2306.17136 [astro-ph.CO] .
  44. Y. Bai, T.-K. Chen,  and M. Korwar, “QCD-Collapsed Domain Walls: QCD Phase Transition and Gravitational Wave Spectroscopy,”   (2023), arXiv:2306.17160 [hep-ph] .
  45. E. Megias, G. Nardini,  and M. Quiros, “Pulsar Timing Array Stochastic Background from light Kaluza-Klein resonances,”   (2023), arXiv:2306.17071 [hep-ph] .
  46. J.-Q. Jiang, Y. Cai, G. Ye,  and Y.-S. Piao, “Broken blue-tilted inflationary gravitational waves: a joint analysis of NANOGrav 15-year and BICEP/Keck 2018 data,”   (2023), arXiv:2307.15547 [astro-ph.CO] .
  47. Z. Zhang, C. Cai, Y.-H. Su, S. Wang, Z.-H. Yu,  and H.-H. Zhang, “Nano-Hertz gravitational waves from collapsing domain walls associated with freeze-in dark matter in light of pulsar timing array observations,”   (2023), arXiv:2307.11495 [hep-ph] .
  48. D. G. Figueroa, M. Pieroni, A. Ricciardone,  and P. Simakachorn, “Cosmological Background Interpretation of Pulsar Timing Array Data,”   (2023), arXiv:2307.02399 [astro-ph.CO] .
  49. L. Bian, S. Ge, J. Shu, B. Wang, X.-Y. Yang,  and J. Zong, “Gravitational wave sources for Pulsar Timing Arrays,”  (2023), arXiv:2307.02376 [astro-ph.HE] .
  50. X. Niu and M. H. Rahat, “NANOGrav signal from axion inflation,”   (2023), arXiv:2307.01192 [hep-ph] .
  51. P. F. Depta, K. Schmidt-Hoberg,  and C. Tasillo, “Do pulsar timing arrays observe merging primordial black holes?”  (2023), arXiv:2306.17836 [astro-ph.CO] .
  52. K. T. Abe and Y. Tada, “Translating nano-Hertz gravitational wave background into primordial perturbations taking account of the cosmological QCD phase transition,”   (2023), arXiv:2307.01653 [astro-ph.CO] .
  53. G. Servant and P. Simakachorn, “Constraining Post-Inflationary Axions with Pulsar Timing Arrays,”   (2023), arXiv:2307.03121 [hep-ph] .
  54. J. Ellis, M. Fairbairn, G. Franciolini, G. Hütsi, A. Iovino, M. Lewicki, M. Raidal, J. Urrutia, V. Vaskonen,  and H. Veermäe, “What is the source of the PTA GW signal?”  (2023b), arXiv:2308.08546 [astro-ph.CO] .
  55. N. Bhaumik, R. K. Jain,  and M. Lewicki, “Ultra-low mass PBHs in the early universe can explain the PTA signal,”   (2023), arXiv:2308.07912 [astro-ph.CO] .
  56. W. Ahmed, T. A. Chowdhury, S. Nasri,  and S. Saad, “Gravitational waves from metastable cosmic strings in Pati-Salam model in light of new pulsar timing array data,”   (2023), arXiv:2308.13248 [hep-ph] .
  57. S. J. Chamberlin and X. Siemens, “Stochastic backgrounds in alternative theories of gravity: overlap reduction functions for pulsar timing arrays,” Phys. Rev. D 85, 082001 (2012), arXiv:1111.5661 [astro-ph.HE] .
  58. W. Qin, K. K. Boddy, M. Kamionkowski,  and L. Dai, “Pulsar-timing arrays, astrometry, and gravitational waves,” Phys. Rev. D 99, 063002 (2019), arXiv:1810.02369 [astro-ph.CO] .
  59. W. Qin, K. K. Boddy,  and M. Kamionkowski, “Subluminal stochastic gravitational waves in pulsar-timing arrays and astrometry,” Phys. Rev. D 103, 024045 (2021), arXiv:2007.11009 [gr-qc] .
  60. K.-W. Ng, “Redshift-space fluctuations in stochastic gravitational wave background,” Phys. Rev. D 106, 043505 (2022), arXiv:2106.12843 [astro-ph.CO] .
  61. Z.-C. Chen, C. Yuan,  and Q.-G. Huang, “Non-tensorial gravitational wave background in NANOGrav 12.5-year data set,” Sci. China Phys. Mech. Astron. 64, 120412 (2021), arXiv:2101.06869 [astro-ph.CO] .
  62. G.-C. Liu and K.-W. Ng, “Timing-residual power spectrum of a polarized stochastic gravitational-wave background in pulsar-timing-array observation,” Phys. Rev. D 106, 064004 (2022), arXiv:2201.06767 [gr-qc] .
  63. Y. Hu, P.-P. Wang, Y.-J. Tan,  and C.-G. Shao, “Full analytic expression of overlap reduction function for gravitational wave background with pulsar timing arrays,”   (2022), arXiv:2205.09272 [gr-qc] .
  64. R. C. Bernardo and K.-W. Ng, “Stochastic gravitational wave background phenomenology in a pulsar timing array,” Phys. Rev. D 107, 044007 (2023b), arXiv:2208.12538 [gr-qc] .
  65. Q. Liang and M. Trodden, “Detecting the stochastic gravitational wave background from massive gravity with pulsar timing arrays,” Phys. Rev. D 104, 084052 (2021), arXiv:2108.05344 [astro-ph.CO] .
  66. R. C. Bernardo and K.-W. Ng, “Looking out for the Galileon in the nanohertz gravitational wave sky,” Phys. Lett. B 841, 137939 (2023c), arXiv:2206.01056 [astro-ph.CO] .
  67. R. C. Bernardo and K.-W. Ng, “Constraining gravitational wave propagation using pulsar timing array correlations,” Phys. Rev. D 107, L101502 (2023d), arXiv:2302.11796 [gr-qc] .
  68. Y.-M. Wu, Z.-C. Chen,  and Q.-G. Huang, “Search for stochastic gravitational-wave background from massive gravity in the NANOGrav 12.5-year dataset,” Phys. Rev. D 107, 042003 (2023), arXiv:2302.00229 [gr-qc] .
  69. Q. Liang, M.-X. Lin,  and M. Trodden, “A Test of Gravity with Pulsar Timing Arrays,”   (2023), arXiv:2304.02640 [astro-ph.CO] .
  70. R. C. Bernardo and K.-W. Ng, “Testing gravity with cosmic variance-limited pulsar timing array correlations,”   (2023e), arXiv:2306.13593 [gr-qc] .
  71. K. J. Lee, “Pulsar Timing Arrays and Gravity Tests in the Radiative Regime,” Class. Quant. Grav. 30, 224016 (2013), arXiv:1404.2090 [astro-ph.CO] .
  72. D. P. Mihaylov, C. J. Moore, J. Gair, A. Lasenby,  and G. Gilmore, “Astrometric effects of gravitational wave backgrounds with nonluminal propagation speeds,” Phys. Rev. D 101, 024038 (2020), arXiv:1911.10356 [gr-qc] .
  73. T. Clifton, P. G. Ferreira, A. Padilla,  and C. Skordis, “Modified Gravity and Cosmology,” Phys. Rept. 513, 1–189 (2012), arXiv:1106.2476 [astro-ph.CO] .
  74. A. Joyce, B. Jain, J. Khoury,  and M. Trodden, “Beyond the Cosmological Standard Model,” Phys. Rept. 568, 1–98 (2015), arXiv:1407.0059 [astro-ph.CO] .
  75. S. Nojiri, S. D. Odintsov,  and V. K. Oikonomou, “Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution,” Phys. Rept. 692, 1–104 (2017), arXiv:1705.11098 [gr-qc] .
  76. N. J. Cornish, L. O’Beirne, S. R. Taylor,  and N. Yunes, “Constraining alternative theories of gravity using pulsar timing arrays,” Phys. Rev. Lett. 120, 181101 (2018), arXiv:1712.07132 [gr-qc] .
  77. R. Kase and S. Tsujikawa, “Dark energy in Horndeski theories after GW170817: A review,” Int. J. Mod. Phys. D 28, 1942005 (2019), arXiv:1809.08735 [gr-qc] .
  78. P. G. Ferreira, “Cosmological Tests of Gravity,” Ann. Rev. Astron. Astrophys. 57, 335–374 (2019), arXiv:1902.10503 [astro-ph.CO] .
  79. L. O’Beirne, N. J. Cornish, S. J. Vigeland,  and S. R. Taylor, “Constraining alternative polarization states of gravitational waves from individual black hole binaries using pulsar timing arrays,” Phys. Rev. D 99, 124039 (2019), arXiv:1904.02744 [gr-qc] .
  80. G. Tasinato, “Kinematic anisotropies and pulsar timing arrays,”   (2023), arXiv:2309.00403 [gr-qc] .
  81. L. Hui, A. Nicolis,  and C. Stubbs, “Equivalence Principle Implications of Modified Gravity Models,” Phys. Rev. D 80, 104002 (2009), arXiv:0905.2966 [astro-ph.CO] .
  82. J. Wang, L. Hui,  and J. Khoury, “No-Go Theorems for Generalized Chameleon Field Theories,” Phys. Rev. Lett. 109, 241301 (2012), arXiv:1208.4612 [astro-ph.CO] .
  83. C. de Rham, “Galileons in the Sky,” Comptes Rendus Physique 13, 666–681 (2012), arXiv:1204.5492 [astro-ph.CO] .
  84. P. Brax, C. Burrage,  and A.-C. Davis, “Laboratory Tests of the Galileon,” JCAP 09, 020 (2011), arXiv:1106.1573 [hep-ph] .
  85. A. Ali, R. Gannouji, M. W. Hossain,  and M. Sami, “Light mass galileons: Cosmological dynamics, mass screening and observational constraints,” Phys. Lett. B 718, 5–14 (2012), arXiv:1207.3959 [gr-qc] .
  86. M. Andrews, Y.-Z. Chu,  and M. Trodden, “Galileon forces in the Solar System,” Phys. Rev. D 88, 084028 (2013), arXiv:1305.2194 [astro-ph.CO] .
  87. C. de Rham and S. Melville, “Gravitational Rainbows: LIGO and Dark Energy at its Cutoff,” Phys. Rev. Lett. 121, 221101 (2018), arXiv:1806.09417 [hep-th] .
  88. J. Nay, K. K. Boddy, T. L. Smith,  and C. M. F. Mingarelli, “Harmonic Analysis for Pulsar Timing Arrays,”   (2023), arXiv:2306.06168 [gr-qc] .
  89. S. Wang and Z.-C. Zhao, “Unveiling the Graviton Mass Bounds through Analysis of 2023 Pulsar Timing Array Datasets,”   (2023), arXiv:2307.04680 [astro-ph.HE] .
  90. J. E. Kim, B. Kyae,  and H. M. Lee, “Effective Gauss-Bonnet interaction in Randall-Sundrum compactification,” Phys. Rev. D 62, 045013 (2000), arXiv:hep-ph/9912344 .
  91. J. E. Kim and H. M. Lee, “Gravity in the Einstein-Gauss-Bonnet theory with the Randall-Sundrum background,” Nucl. Phys. B 602, 346–366 (2001), [Erratum: Nucl.Phys.B 619, 763–764 (2001)], arXiv:hep-th/0010093 .
  92. L. Capuano, L. Santoni,  and E. Barausse, “Black hole hairs in scalar-tensor gravity (and lack thereof),”   (2023), arXiv:2304.12750 [gr-qc] .
  93. K. Aoki and S. Tsujikawa, “Coupled vector Gauss-Bonnet theories and hairy black holes,” Phys. Lett. B 843, 138022 (2023), arXiv:2303.13717 [gr-qc] .
  94. M. Isi and A. J. Weinstein, “Probing gravitational wave polarizations with signals from compact binary coalescences,”   (2017), arXiv:1710.03794 [gr-qc] .
  95. B. P. Abbott et al. (LIGO Scientific, Virgo), “GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence,” Phys. Rev. Lett. 119, 141101 (2017), arXiv:1709.09660 [gr-qc] .
  96. B. P. Abbott et al. (LIGO Scientific, Virgo), “Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background,” Phys. Rev. Lett. 120, 201102 (2018), arXiv:1802.10194 [gr-qc] .
  97. J. H. Taylor, L. A. Fowler,  and P. M. McCulloch, “Measurements of general relativistic effects in the binary pulsar PSR 1913+16,” Nature 277, 437–440 (1979).
  98. W. van Straten, M. Bailes, M. C. Britton, S. R. Kulkarni, S. B. Anderson, R. N. Manchester,  and J. Sarkissian, “A Test of General Relativity from the three-dimensional orbital geometry of a binary pulsar,” Nature 412, 158–160 (2001), arXiv:astro-ph/0108254 .
  99. I. Ciufolini and E. C. Pavlis, “A confirmation of the general relativistic prediction of the Lense-Thirring effect,” Nature 431, 958–960 (2004).
  100. M. J. Valtonen et al., “A massive binary black-hole system in OJ 287 and a test of general relativity,” Nature 452, 851–853 (2008), arXiv:0809.1280 [astro-ph] .
  101. R. Reyes et al., “Confirmation of general relativity on large scales from weak lensing and galaxy velocities,” Nature 464, 256–258 (2010), arXiv:1003.2185 [astro-ph.CO] .
  102. M. Coleman Miller and N. Yunes, “The new frontier of gravitational waves,” Nature 568, 469–476 (2019).
  103. R. C. Bernardo and K.-W. Ng, “PTAfast: PTA correlations from stochastic gravitational wave background,” Astrophysics Source Code Library, record ascl:2211.001 (2022).
  104. K.-W. Ng and G.-C. Liu, “Correlation functions of CMB anisotropy and polarization,” Int. J. Mod. Phys. D 8, 61–83 (1999), arXiv:astro-ph/9710012 .
  105. W. J. Handley, M. P. Hobson,  and A. N. Lasenby, “PolyChord: nested sampling for cosmology,” Mon. Not. Roy. Astron. Soc. 450, L61–L65 (2015), arXiv:1502.01856 [astro-ph.CO] .
  106. W. J. Handley, M. P. Hobson,  and A. N. Lasenby, “POLYCHORD: next-generation nested sampling,” Mon. Not. Roy. Astron. Soc. 453, 4384–4398 (2015), arXiv:1506.00171 [astro-ph.IM] .
  107. J. Torrado and A. Lewis, “Cobaya: Code for Bayesian Analysis of hierarchical physical models,” JCAP 05, 057 (2021), arXiv:2005.05290 [astro-ph.IM] .
  108. A. Lewis, “GetDist: a Python package for analysing Monte Carlo samples,”   (2019), arXiv:1910.13970 [astro-ph.IM] .
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