Testing General Relativity Using the Evolution of Linear Bias

TL;DR

This paper models the evolution of linear bias in the universe considering Hubble scale effects within General Relativity, proposing a method to test GR through observable galaxy clustering data.

Contribution

It provides an analytical derivation of scale-dependent bias evolution incorporating Hubble scale effects and links it to observational tests of General Relativity.

Findings

Scale dependence due to Hubble effects is minimal up to galaxy cluster scales.

The model connects the matter growth index to observable clustering parameters.

Proposes a novel observational test for GR on extragalactic scales.

Abstract

We investigate the cosmic evolution of the linear bias in the framework of a flat FLRW spacetime. We consider metric perturbations in the Newtonian gauge, including Hubble scale effects. Making the following assumptions, (i) scale independent current epoch bias $b_0$, (ii) equal accelerations between tracers and matter, (iii) unimportant halo merging effects (which is quite accurate for $z<3$), we analytically derive the scale dependent bias evolution. The identified scale dependence is only due to Hubble scale evolution GR effects, while other scale dependence contributions are ignored. We find that up to galaxy cluster scales the fluctuations of the metric do not introduce a significant scale dependence in the linear bias. Our bias evolution model is then used to derive a connection between the matter growth index $\gamma$ and the observable value of the tracer power spectrum normalization $\sigma_8(z)$. We show how this connection can be used as an observational test of General Relativity on extragalactic scales.