Modified Gravity Constraints from the Full Shape Modeling of Clustering Measurements from DESI 2024 (2411.12026v2)

Abstract: We present cosmological constraints on deviations from general relativity (GR) from the first-year of clustering observations from the Dark Energy Spectroscopic Instrument (DESI) in combination with other datasets. We first consider the $\mu(a,k)$-$\Sigma(a,k)$ modified gravity (MG) parametrization (as well as $\eta(a,k)$) in flat $\Lambda$CDM and $w_0 w_a$CDM backgrounds. Using a functional form for time-only evolution gives $\mu_0= 0.11^{+0.44}_{-0.54}$ from DESI(FS+BAO)+BBN and a wide prior on $n_{s}$. Using DESI(FS+BAO)+CMB+DESY3+DESY5-SN, we obtain $\mu_0 = 0.05\pm 0.22$ and $\Sigma_0 = 0.008\pm 0.045$ in the $\Lambda$CDM background. In $w_0 w_a$CDM, we obtain $\mu_0 =-0.24^{+0.32}_{-0.28}$ and $\Sigma_0 = 0.006\pm 0.043$, consistent with GR, and we still find a preference of the data for dynamical dark energy with $w_0>-1$ and $w_a<0$. We then use binned forms in the two backgrounds starting with two bins in redshift and then combining them with two bins in scale for a total of 4 and 8 MG parameters, respectively. All MG parameters are found consistent with GR. We also find that the tension reported for $\Sigma_0$ with GR when using Planck PR3 goes away when we use the recent LoLLiPoP+HiLLiPoP likelihoods. As noted previously, this seems to indicate that the tension is related to the CMB lensing anomaly in PR3 which is also resolved when using these likelihoods. We then constrain the class of Horndeski theory in the effective field theory of dark energy. We consider both EFT-basis and $\alpha$-basis. Assuming a power law parametrization for the function $\Omega$, which controls non-minimal coupling, we obtain $\Omega_0 = 0.012^{+0.001}_{-0.012}$ and $s_0 = 0.996^{+0.54}_{-0.20}$ from DESI(FS+BAO)+DESY5SN+CMB in a $\Lambda$CDM background. Similar results are obtained when using the $\alpha$-basis, where we constrain $c_M<1.14$, and are all consistent with GR. [Abridged.]

• The paper presents a rigorous full-shape modeling analysis of DESI clustering data to constrain modified gravity parameters using the μ-Σ formalism.
• It combines DESI observations with CMB, DESY3 weak lensing, and DESY5 supernova data to break parameter degeneracies and refine limits on GR deviations.
• The paper leverages the EFT framework and binned approaches to explore dynamical dark energy and potential non-zero contributions, affirming consistency with GR.

Overview of Cosmological Constraints on Modified Gravity from DESI Clustering Data

This paper rigorously investigates the constraints on deviations from General Relativity (GR) using clustering measurements from the Dark Energy Spectroscopic Instrument (DESI). By leveraging the full-shape modeling of the power spectrum and combining it with other cosmological datasets, such as CMB and supernovae data, the authors provide a detailed examination of modified gravity (MG) parameters within the context of cosmological scale tests.

Key Contributions and Methodologies:

The paper employs both phenomenological and effective field theory approaches to explore potential deviations from GR. Key methodologies include:

1. Parametrization of Modified Gravity: The authors adopt the frequently used $\mu(a,k) - \Sigma(a,k)$ formalism to test deviations from GR. The $\mu$ parameter typically enters equations governing massive particle dynamics, while $\Sigma$ pertains to massless particles, crucial for gravitational lensing surveys.
2. Functional and Binned Parametrizations: The research explores MG parameters through both functional forms in redshift and scale, and binned approaches. This dual approach allows for a comprehensive examination of possible GR deviations, leveraging the full sensitivity of DESI's clustering data.
3. Combination with External Datasets: The analysis integrates DESI clustering data with CMB data from Planck (and ACT for lensing), DES Year 3 (DESY3) galaxy weak lensing, and supernova data from DESY5. These combinations are pivotal for breaking parameter degeneracies and improving constraint precision.
4. EFT Framework: The Effective Field Theory (EFT) approach is employed to model dark energy in a unified manner, analyzing options within both EFT and $\alpha$-basis parametrizations. The focus lies on constraining parameters related to the evolution of linear perturbations and the effective Planck mass.

Significant Findings:

• In the $\mu-\Sigma$ framework using a $\Lambda$CDM background, DESI data in combination with other datasets yields constraints on $\mu$ and $\Sigma$ close to GR predictions. The best constraints on these MG parameters, largely free from systematic effects like the CMB lensing anomaly, come from combining DESI with Planck LoLLiPoP+HiLLiPoP likelihoods, DESY3, and DESY5 supernova data.
• When considering a $w_0w_a$CDM background, the data shows a slight preference for dynamical dark energy, though MG parameters remain consistent with GR.
• The analysis using EFT and $\alpha$-basis provides further constraints, showing consistency with GR but highlighting possible non-zero contributions from parameters like the braiding term. There is a noted correlation between negative indications from past CMB lens findings and systematics possibly related to Planck data.
• Binned analyses in both redshift and scale show the potential for increasingly tighter constraints with future data, suggesting further exploration of MG theories on these fronts.

Implications and Future Directions:

The paper underscores DESI's pivotal role in testing GR at cosmological scales with its extensive clustering data, expected to improve constraints on MG parameters significantly in the coming years. The potential to refine constraints on $\mu$, currently less precise than $\Sigma$, will be a focal development as DESI data accumulates.

Furthermore, the investigation of alternative parametrizations and their stability conditions enriches the understanding of MG theories' validity. The impact of the latest CMB likelihoods, correcting for previous anomalies, sets new benchmarks for assessing the fundamental gravitational framework.

Future analyses should consider the full incorporation of cross-correlation datasets and explore further parametrization complexities, especially in the scale dependence of MG parameters, to enhance the robustness and granularity of cosmological GR tests. This paper serves as a comprehensive reference for the state-of-the-art in cosmological constraints on MG, offering paths and questions for ongoing research in the field.