Constraining gravity with the decay rate of cosmological gravitational potential

TL;DR

The paper addresses the challenge of testing general relativity at cosmological scales to distinguish dark energy from modified gravity by exploiting the decay rate (DR) of the cosmological gravitational potential, which is sensitive to gravity and largely free from key astrophysical systematics. It analyzes DR measurements from the DR9 DESI imaging surveys and Planck CMB maps to constrain four one-parameter MG extensions to flat $Λ$CDM: a growth-rate form $f=\Omega_m^\gamma(a)$ and three $\Sigma(a)$-based $G_{\rm eff}$ models with $\eta=1$. The results yield $\gamma = 0.47^{+0.22}_{-0.15}$, consistent with GR ($\gamma \simeq 0.55$), and $\Sigma_Λ = 0.018^{+0.052}_{-0.053}$, $\Sigma_1 = 0.020^{+0.065}_{-0.062}$, $\Sigma_2 = 0.027^{+0.067}_{-0.069}$, all compatible with GR ($\Sigma=0$) across parameterizations; the DR constraints are already competitive with other probes and are expected to improve by a factor of ~2 with future full-sky surveys. The work demonstrates the promise of DR as a robust, relatively model-flexible probe of gravity, complementary to other large-scale structure measurements, and highlights prospects for tighter bounds on gravity modifications when DR is combined with additional probes like RSD and lensing.

Abstract

A key task in cosmology is to test the validity of general relativity (GR) at cosmological scales and, therefore, to distinguish between dark energy and modified gravity (MG) as the driver of the late-time cosmic acceleration. The decay rate ($DR$) of cosmological gravitational potential, being sensitive to gravity and being immune to various astrophysical uncertainties, enables GR tests independent to other structure growth probes. Recently we have measured $DR$ at $0.2\leq z\leq 1.4$, combining the DR9 galaxy catalog from the DESI imaging surveys and Planck cosmic microwave background maps \citep{arXiv:2411.12594}. Here we use this measurement to test gravity, and restrict the analysis to one-parameter extensions to the standard $Λ$CDM cosmology. We consider four one-parameter MG parameterizations. One is $f(a)=Ω_m^γ(a)$. The other three adopt the gravitational slip parameter $η=1$ and consider variations in the effective gravitational constant $G_{\rm eff}/G$ with the parameterization $Σ(a)=Σ_ΛΩ_Λ(a)/Ω_Λ$, $Σ(a)=Σ_1 a$ or $Σ(a)=Σ_2 a^2$. We find $γ=0.47^{+0.22}_{-0.15}$, consistent with the GR prediction $γ\simeq 0.55$. We also find $Σ_Λ=0.018^{+0.052}_{-0.053}$, $Σ_1=0.020^{+0.065}_{-0.062}$, and $Σ_2=0.027^{+0.067}_{-0.069}$, fully consistent with the GR case of $Σ=0$, regardless of parameterizations of $Σ(a)$. The constraining power is already competitive, while a factor of 2 further improvement is expected for the upcoming full-sky galaxy surveys.

Figures (4)

• Figure 1: Constraint on the $\gamma$ parameter using $DR$. The shaded areas indicate the $68\%$ confidence region. $\gamma=0.47_{-0.15}^{+0.22}$, consistent with the GR value of $\gamma\simeq 0.55$.
• Figure 2: $\gamma$ constraints from various data sets. In the bottom is $\gamma$ constrained by $DR$. The constraint labeled with "Artis et al" is from Artis24 using cluster number counts. The one with label "$S_8$" is calculated by all the $S_8(z)$ measured by Fig.19 of Qu24 (includes $S_8(z)$ measurements of Qu24Sailer24Farren_2024 ). The other constraints are calculated by disregarding one or two data points.
• Figure 3: Similar to Fig.\ref{['fig.gammas_conf']}, but for the $\Sigma_\Lambda$, $\Sigma_1$ and $\Sigma_2$ parameterizations.
• Figure 4: The dependence of MG parameter constraints on $\Omega_m$. Over the range of bestfit $\Omega_m$ from BAO, CMB and SNe Ia, the induced variation in $\gamma$ and $\Sigma_\Lambda$ is subdominant to the statistical error, and the agreement with GR remains unchanged.