Rescuing constraints on modified gravity using gravitational redshift in large-scale structure

TL;DR

This paper demonstrates that gravitational redshift measurements can break degeneracies in testing modified gravity theories using galaxy distributions, which are otherwise limited by assumptions about dark matter's equivalence principle.

Contribution

It introduces a novel method to constrain modified gravity by using gravitational redshift, overcoming degeneracies present in traditional redshift-space distortion analyses.

Findings

Gravitational redshift can break degeneracies in modified gravity constraints.

Relaxing the weak equivalence principle for dark matter degrades existing constraints.

Upcoming surveys will enable detection of gravitational redshift effects.

Abstract

The distribution of galaxies provides an ideal laboratory to test for deviations from General Relativity. In particular, redshift-space distortions are commonly used to constrain modifications to the Poisson equation, which governs the strength of dark matter clustering. Here, we show that these constraints rely on the validity of the weak equivalence principle, which has never been tested for the dark matter component. Relaxing this restrictive assumption leads to modifications in the growth of structure that are fully degenerate with modifications induced by the Poisson equation. This in turns strongly degrades the constraining power of redshift-space distortions. Such degeneracies can however be broken and tight constraints on modified gravity can be recovered by measuring gravitational redshift from the galaxy distribution, an effect that will be detectable by the coming generation of large-scale structure surveys.