Prospects for measuring the relative velocities of galaxy clusters in
  photometric surveys using the kinetic Sunyaev-Zel'dovich Effect
  We consider the prospects for measuring the pairwise kinetic
Sunyaev-Zel'dovich (kSZ) signal from galaxy clusters discovered in large
photometric surveys such as the Dark Energy Survey (DES). We project that the
DES cluster sample will, in conjunction with existing mm-wave data from the
South Pole Telescope (SPT), yield a detection of the pairwise kSZ signal at the
8-13 sigma level, with sensitivity peaking for clusters separated by ~100 Mpc
distances. A next-generation version of SPT would allow for a 18-30 sigma
detection and would be limited by variance from the kSZ signal itself and
residual thermal Sunyaev-Zel'dovich (tSZ) signal. Throughout our analysis we
assume photometric redshift errors, which wash out the signal for clusters
separated by <~50 Mpc; a spectroscopic survey of the DES sample would recover
this signal and allow for a 26-43 sigma detection, and would again be limited
by kSZ/tSZ variance. Assuming a standard model of structure formation, these
high-precision measurements of the pairwise kSZ signal will yield detailed
information on the gas content of the galaxy clusters. Alternatively, if the
gas can be sufficiently characterized by other means (e.g. using tSZ, X-ray, or
weak lensing), then the relative velocities of the galaxy clusters can be
isolated, thereby providing a precision measurement of gravity on 100 Mpc
scales. We briefly consider the utility of these measurements for constraining
theories of modified gravity.
