Distinguishing screening mechanisms with environment-dependent velocity
  statistics
  Alternative theories of gravity typically invoke an environment-dependent
screening mechanism to allow phenomenologically interesting deviations from
general relativity (GR) to manifest on larger scales, while reducing to GR on
small scales. The observation of the transition from screened to unscreened
behavior would be compelling evidence for beyond-GR physics. We show that
pairwise peculiar velocity statistics, in particular the relative radial
velocity dispersion, $\sigma_\parallel$ , can be used to observe this
transition when they are binned by some measure of halo environment. We
established this by measuring the radial velocity dispersion between pairs of
halos in N-body simulations for three $f(R)$ gravity and four symmetron models.
We developed an estimator involving only line-of-sight velocities to show that
this quantity is observable, and binned the results in halo mass, ambient
density, and the isolatedness of halos. Ambient density is found to be the most
relevant measure of environment; it is distinct from isolatedness, and
correlates well with theoretical expectations for the symmetron model. By
binning $\sigma_\parallel$ in ambient density, we find a strong
environment-dependent signature for the symmetron models, with the velocities
showing a clear transition from GR to non-GR behavior. No such transition is
observed for $f(R)$, as the relevant scales are deep in the unscreened regime.
Observations of the relative radial velocity dispersion in forthcoming peculiar
velocity surveys, if binned appropriately by environment, therefore offer a
valuable way of detecting the screening signature of modified gravity.
