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.
