Constraints on gravity and dark energy from the pairwise kinematic Sunyaev-Zeldovich effect

We calculate the constraints on dark energy and cosmic modifications to gravity achievable with upcoming cosmic microwave background (CMB) surveys sensitive to the Sunyaev-Zeldovich (SZ) effects. The analysis focuses on using the mean pairwise velocity of clusters as observed through the kinematic SZ effect (kSZ), an approach based on the same methods used for the first detection of the kSZ effect, and includes a detailed derivation and discussion of this statistic's covariance under a variety of different survey assumptions. The potential of current, Stage II, and upcoming, Stage III and Stage IV, CMB observations are considered, in combination with contemporaneous spectroscopic and photometric galaxy observations. A detailed assessment is made of the sensitivity to the assumed statistical and systematic uncertainties in the optical depth determination, the magnitude and uncertainty in the minimum detectable mass, and the importance of pairwise velocity correlations at small separations, where non-linear effects can start to arise. In combination with Stage III constraints on the expansion history, such as those projected by the Dark Energy Task Force, we forecast 5\% and 2\% for fractional errors on the growth factor, $\gamma$, for Stage III and Stage IV surveys respectively, and 2\% constraints on the growth rate, $f_g$, for a Stage IV survey for $0.2<z<0.6$. The results suggest that kSZ measurements of cluster peculiar velocities, obtained from cross-correlation with upcoming spectroscopic galaxy surveys, could provide robust tests of dark energy and theories of gravity on cosmic scales.