Testing gravity on cosmological scales with cosmic shear, cosmic microwave background anisotropies, and redshift-space distortions

We use a range of cosmological data to constrain phenomenological modifications to general relativity on cosmological scales, through modifications to the Poisson and lensing equations. We include cosmic microwave background anisotropy measurements from the Planck satellite, cosmic shear from CFHTLenS and DES-SV, and redshift-space distortions from BOSS data release 12 and the 6dF galaxy survey. We find no evidence of departures from general relativity, with the modified gravity parameters constrained to $\Sigma_0 = 0.05^{+0.05}_{-0.07}$ and $\mu_0 = -0.10^{+0.20}_{-0.16}$, where $\Sigma_0$ and $\mu_0$ refer to deviations from general relativity today and are defined to be zero in general relativity. We also forecast the sensitivity to those parameters of the full five-year Dark Energy Survey and of an experiment like the Large Synoptic Survey Telescope, showing a substantial expected improvement in the constraint on $\Sigma_0$.