New constraints on $f(R)$ gravity from clusters of galaxies
  The abundance of massive galaxy clusters is a powerful probe of departures
from General Relativity (GR) on cosmic scales. Despite current stringent
constraints placed by stellar and galactic tests, on larger scales alternative
theories of gravity such as $f(R)$ can still work as effective theories. Here
we present constraints on two popular models of $f(R)$, Hu-Sawicki and
"designer", derived from a fully self-consistent analysis of current samples of
X-ray selected clusters and accounting for all the covariances between
cosmological and astrophysical parameters. Using cluster number counts in
combination with recent data from the cosmic microwave background (CMB) and the
CMB lensing potential generated by large scale structures, as well as with
other cosmological constraints on the background expansion history and its mean
matter density, we obtain the upper bounds $\log_{10}|f_{R0}| < 4.79$ and
$\log_{10}B_0 < 3.75$ at the 95.4 per cent confidence level, for the Hu-Sawicki
(with $n=1$) and designer models, respectively. The robustness of our results
derives from high quality cluster growth data for the most massive clusters
known out to redshifts $z \sim 0.5$, a tight control of systematic
uncertainties including an accurate and precise mass calibration from weak
gravitational lensing data, and the use of the full shape of the halo mass
function over the mass range of our data.
