Constraints on modified gravity from Sunyaev-Zeldovich cluster surveys

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 South Pole Telescope (SPT), Planck, SPT polarimeter (SPTpol), and Atacama Cosmology Telescope polarimeter (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 4, to σ_f_(R0)=2×10^(-5) (68% confidence level) while SPT, SPTpol, and ACTpol yield about 3×10^(-5). Adding the cluster power spectrum further improves the constraints to σ_f_(R0)=5×10^(-6) for Planck and σ_f_(R0)=2×10^(-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.