Next Generation Redshift Surveys and the Origin of Cosmic Acceleration

TL;DR

This paper proposes a null test parameter for cosmic acceleration explanations, demonstrating how upcoming surveys can distinguish between dark energy within GR and modified gravity models by measuring structure growth with high precision.

Contribution

It introduces a null test parameter based on observable quantities to differentiate dark energy from modified gravity, and assesses the sensitivity of future surveys to this test.

Findings

Null test parameter $oldsymbol{\epsilon(k,a)}$ can be expressed in terms of observable bias and redshift space distortions.

Future surveys like SDSS III and ADEPT can test structure growth predictions to better than 1%.

Modified gravity models like $f(R)$ predict different scale and redshift dependence of growth rate.

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 $\epsilon(k,a) \equiv\Omega_m^{- \gamma} d \ln D / d \ln a - 1$, where $a$ is the scale factor, $D$ is the growth rate of structure, $\Omega_m(a)$ is the matter density parameter, and $\gamma$ 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, $\beta(k,a)$. Measurements of the CMB power spectrum determine $\Omega_{m 0} H_0^2$. If dark energy within GR is the solution to the cosmic acceleration problem, then the logarithmic growth rate of structure $d \ln D / d \ln a = \Omega_m^\gamma$. Thus, $\epsilon(k,a) =0$ 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 $\beta$ 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.