Constraining f (R) gravity with Sunyaev-Zel'dovich clusters detected by the Planck satellite

Clusters of galaxies have the potential of providing powerful constraints on possible deviations from General Relativity. We use the catalog of Sunyaev-Zel'dovich (SZ) sources detected by Planck and consider a correction to the halo mass function for a f(R) class of modified gravity models, which has been recently found to reproduce well results from N-body simulations, to place constraints on the scalaron field amplitude at the present time, fR0. We find that applying this correction to different calibrations of the halo mass function produces upper bounds on fR0 tighter by more than an order of magnitude, ranging from log10(-fR0)<-5.81 to log10(-fR0)<-4.40 (95% confidence level). This sensitivity is due to the different shape of the halo mass function, which is degenerate with the parameters used to calibrate the scaling relations between SZ observables and cluster masses. Any claim of constraints more stringent that the weaker limit above, based on cluster number counts, appears to be premature and must be supported by a careful calibration of the halo mass function and by a robust calibration of the mass scaling relations.