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