The velocity field of dark matter and galaxies reflects the continued action of gravity throughout cosmic history. We show that the low-order moments of the pairwise velocity distribution, $v_{ 12}$, are a powerful diagnostic of the laws of gravity on cosmological scales. In particular, the projected line-of-sight galaxy pairwise velocity dispersion, $\sigma_{ 12}(r)$, is very sensitive to the presence of modified gravity. Using a set of high-resolution N-body simulations we compute the pairwise velocity distribution and its projected line-of-sight dispersion for a class of modified gravity theories: the chameleon \fR gravity and Galileon gravity (cubic and quartic). The velocities of dark matter halos with a wide range of masses would exhibit deviations from General Relativity at the $(5-10)\sigma$ level. We examine strategies for detecting these deviations in galaxy redshift and peculiar velocity surveys. If detected, this signature would be a "smoking gun" for modified gravity.
Categories: astro-ph.CO