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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, $σ_\parallel$ , 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 $σ_\parallel$ 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.