Next Generation Redshift Surveys and the Origin of Cosmic Acceleration

TL;DR

The paper proposes a null test, $\epsilon(k,a)$, for General Relativity by tying the growth rate of cosmic structure to the expansion history and galaxy bias, enabling a model-independent test of gravity using future redshift surveys and CMB lensing data. It analyzes $f(R)$ gravity within the PPF formalism to predict scale- and redshift-dependent growth, contrasting it with GR where growth follows $\Omega_m^{\gamma}$. By jointly measuring the redshift-space distortion parameter $\beta(k,a)$ and the galaxy bias $b(a)$—via cross-correlations with CMB lensing—the study forecasts percent-level constraints on $\epsilon$ for surveys like BOSS and ADEPT, and highlights ADEPT’s potential to detect very small deviations ($B_0 \sim 10^{-4}$). The results emphasize that small-scale measurements provide the strongest leverage on MG, offering a practical pathway to testing gravity on cosmological scales and probing the origin of cosmic acceleration.

Abstract

Cosmologists are exploring two possible sets of explanations for the remarkable observation of cosmic acceleration: dark energy fills space or general relativity fails on cosmological scales. We define a null test parameter $ε(k,a) \equivΩ_m^{- γ} d \ln D / d \ln a - 1$, where $a$ is the scale factor, $D$ is the growth rate of structure, $Ω_m(a)$ is the matter density parameter, and $γ$ is a simple function of redshift. We show that it can be expressed entirely in terms of the bias factor, $b(a)$, (measured from cross-correlations with CMB lensing) and the amplitude of redshift space distortions, $β(k,a)$. Measurements of the CMB power spectrum determine $Ω_{m 0} H_0^2$. If dark energy within GR is the solution to the cosmic acceleration problem, then the logarithmic growth rate of structure $d \ln D / d \ln a = Ω_m^γ$. Thus, $ε(k,a) =0$ on linear scales to better than 1%. We show that in the class of Modified Gravity models known as $f(R)$, the growth rate has a different dependence on scale and redshift. By combining measurements of the amplitude of $β$ and of the bias, $b$, redshift surveys will be able to determine the logarithmic growth rate as a function of scale and redshift. We estimate the predicted sensitivity of the proposed SDSS III (BOSS) survey and the proposed ADEPT mission and find that they will test structure growth in General Relativity to the percent level.

Figures (3)

• Figure 1: The behavior of $\epsilon(k,a)$ = $\Omega_m^{- \gamma} d\ln D/d\ln a - 1$ in GR (solid line) and in $f(R)$ models, as a function of $B_0$ and $k$. Growth is enhanced for $B_0 \ne 0$ and at smaller scales in alternative theories. In GR, $\epsilon (a) = 0$.
• Figure 2: Errors on $P(k)$, normalized to the SDSS-LRG median redshift (z=0.31) for all surveys.
• Figure 3: $\epsilon(k,z)$ for the four surveys, as a factor of $B_0$ and k. Total errorbars around the $\Lambda$CDM case are shown in black; the smaller red errorbars are from bias only.