Redshift Sensitivity of the Kaiser Effect

TL;DR

This paper investigates how the Kaiser effect's sensitivity to redshift impacts testing General Relativity through galaxy motions, emphasizing the importance of low-redshift measurements around z=0.5 for detecting potential modifications to gravity.

Contribution

It analyzes the redshift dependence of the Kaiser effect and identifies the optimal redshift range for testing gravity modifications using galaxy surveys.

Findings

80% of the RSD signal comes from local growth rate at galaxy bin

Redshift z=0.5 offers optimal balance for RSD measurements

Limited synergy between growth and distance measures in cosmology

Abstract

We explore potential strategies for testing General Relativity via the coherent motions of galaxies. Our position at z=0 provides the reference point for distance measures in cosmology. By contrast, the Cosmic Microwave Background at z ~ 1100 acts as the point of reference for the growth of large scale structure. As a result, we find there is a lack of synergy between growth and distance measures. We show that when measuring the gravitational growth index gamma using redshift-space distortions, typically 80% of the signal corresponds to the local growth rate at the galaxy bin location, while the remaining fraction is determined by its behaviour at higher redshifts. In order to clarify whether modified gravity may be responsible for the dark energy phenomenon, the aim is to search for a modification to the growth of structure. One might expect the magnitude of this deviation to be commensurate with the apparent dark energy density Omega_Lambda(z). This provides an incentive to study redshift-space distortions (RSD) at as low a redshift as is practical. Specifically, we find the region around z = 0.5 offers the optimal balance of available volume and signal strength.