  Future multifrequency microwave background experiments with arcminute
resolution and micro-Kelvin temperature sensitivity will be able to detect the
kinetic Sunyaev-Zeldovich (kSZ) 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 degrades only by a factor of two 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 two. 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.
