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The velocity field of dark matter and galaxies reflects the continued actionof gravity throughout cosmic history. We show that the low-order moments of thepairwise velocity distribution, $v_{12}$, are a powerful diagnostic of the lawsof gravity on cosmological scales. In particular, the projected line-of-sightgalaxy pairwise velocity dispersion, $\sigma_{12}(r)$, is very sensitive to thepresence of modified gravity. Using a set of high-resolution N-body simulationswe compute the pairwise velocity distribution and its projected line-of-sightdispersion for a class of modified gravity theories: the chameleon \fR gravityand Galileon gravity (cubic and quartic). The velocities of dark matter haloswith a wide range of masses would exhibit deviations from General Relativity atthe $(5-10)\sigma$ level. We examine strategies for detecting these deviationsin galaxy redshift and peculiar velocity surveys. If detected, this signaturewould be a "smoking gun" for modified gravity.

A clear and measurable signature of modified gravity in the galaxy velocity field