  Upcoming imaging surveys such as the Large Synoptic Survey Telescope will
repeatedly scan large areas of sky and have the potential to yield
million-supernova catalogs. Type Ia supernovae are excellent standard candles
and will provide distance measures that suffice to detect mean pairwise
velocities of their host galaxies. We show that when combining these distance
measures with photometric redshifts for either the supernovae or their host
galaxies, the mean pairwise velocities of the host galaxies will provide a dark
energy probe which is competitive with other widely discussed methods. Adding
information from this test to type Ia supernova photometric luminosity
distances from the same experiment, plus the cosmic microwave background power
spectrum from the Planck satellite, improves the Dark Energy Task Force Figure
of Merit by a factor of 1.8. Pairwise velocity measurements require no
additional observational effort beyond that required to perform the traditional
supernova luminosity distance test, but may provide complementary constraints
on dark energy parameters and the nature of gravity. Incorporating additional
spectroscopic redshift follow-up observations could provide important dark
energy constraints from pairwise velocities alone. Mean pairwise velocities are
much less sensitive to systematic redshift errors than the luminosity distance
test or weak lensing techniques, and also are only mildly affected by
systematic evolution of supernova luminosity.
