We investigate the constraining power of current and future Sunyaev-Zeldovich cluster surveys on the f ( R ) gravity model .
We use a Fisher matrix approach , adopt self-calibration for the mass-observable scaling relation , and evaluate constraints for the SPT , Planck , SPTPol and ACTPol surveys .
The modified gravity effects on the mass function , halo bias , matter power spectrum , and mass-observable relation are taken into account .
We show that , relying on number counts only , the Planck cluster catalog is expected to reduce current upper limits by about a factor of four , to \sigma _ { f _ { R 0 } } = 2 \times 10 ^ { -5 } ( 68 % confidence level ) while SPT , SPTPol and ACTPol yield about 3 \times 10 ^ { -5 } .
Adding the cluster power spectrum further improves the constraints to \sigma _ { f _ { R 0 } } = 5 \times 10 ^ { -6 } for Planck and \sigma _ { f _ { R 0 } } = 2 \times 10 ^ { -5 } for SPTPol , pushing cluster constraints significantly beyond the limit where number counts have no constraining power due to the chameleon screening mechanism .
Further , the combination of both observables breaks degeneracies , especially with the expansion history ( effective dark energy density and equation of state ) .
The constraints are only mildly worsened by the use of self-calibration but depend on the mass threshold and redshift coverage of the cluster samples .