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 _ { R 0 } | < 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 .