Cluster gas fraction as a test of gravity
  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.
