Cluster gas fraction as a test of gravity

TL;DR

This paper introduces a novel cosmological test using galaxy cluster gas fractions to detect deviations from General Relativity, finding that certain $f(R)$ gravity models are inconsistent with observed data.

Contribution

It proposes a new method to test gravity theories by analyzing cluster gas fractions, highlighting potential tensions with specific $f(R)$ models.

Findings

$f(R)$ models with $|ar{f}_{R0}|=3-5\times10^{-5}$ are in tension with observed cluster gas fractions.

The method reveals discrepancies between modified gravity predictions and X-ray cluster data.

Standard assumptions about gas fractions can be used to constrain alternative gravity theories.

Abstract

We propose a new cosmological test of gravity, by using the observed mass fraction of X-ray emitting gas in massive galaxy clusters. The cluster gas fraction, believed to be a fair sample of the average baryon fraction in the Universe, is a well-understood observable, which has previously mainly been used to constrain background cosmology. In some modified gravity models, such as $f(R)$ gravity, gas temperature in a massive cluster is determined by the effective mass of that cluster, which can be larger than its true mass. On the other hand, X-ray luminosity is determined by the true gas density, which in both modified gravity and $\Lambda$CDM models depends mainly on $\Omega_{\rm b}/\Omega_{\rm m}$ and hence the true total cluster mass. As a result, the standard practice of combining gas temperatures and X-ray surface brightnesses of clusters to infer their gas fractions can, in modified gravity models, lead to a larger - in $f(R)$ gravity this can be $1/3$ larger - value of $\Omega_{\rm b}/\Omega_{\rm m}$ than that inferred from other observations such as the CMB. A quick calculation shows that the Hu-Sawicki $n=1$ $f(R)$ model with $|\bar{f}_{R0}|=3\sim5\times10^{-5}$ is in tension with the gas fraction data of the 42 clusters analysed by Allen et al. (2008). We also discuss the implications for other modified gravity models.