  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}fR0 = 3 {\times} 10-5 (68%
confidence level). Adding the cluster power spectrum further improves the
constraints to {\sigma}fR0 = 10-5 for SPT and Planck, and {\sigma}fR0 = 3
{\times} 10-6 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 strongly on the mass threshold of the
cluster samples.
