Dark energy constraints from galaxy cluster peculiar velocities

Future multifrequency microwave background experiments with arcminute resolution and micro-Kelvin temperature sensitivity will be able to detect the kinetic Sunyaev-Zeldovich effect, providing a way to measure radial peculiar velocities of massive galaxy clusters. We show that cluster peculiar velocities have the potential to constrain several dark energy parameters. We compare three velocity statistics (the distribution of radial velocities, the mean pairwise streaming velocity, and the velocity correlation function) and analyze the relative merits of these statistics in constraining dark energy parameters. Of the three statistics, mean pairwise streaming velocity provides constraints that are least sensitive to velocity errors: the constraints on parameters degrade only by a factor of 2 when the random error is increased from 100 to 500 km/s. We also compare cluster velocities with other dark energy probes proposed in the Dark Energy Task Force report. For cluster velocity measurements with realistic priors, the eventual constraints on the dark energy density, the dark energy equation of state and its evolution are comparable to constraints from supernovae measurements, and better than cluster counts and baryon acoustic oscillations; adding velocity to other dark energy probes improves constraints on the figure of merit by more than a factor of 2. For upcoming Sunyaev-Zeldovich galaxy cluster surveys, even velocity measurements with errors as large as 1000 km/s will substantially improve the cosmological constraints compared to using the cluster number density alone.