Testing Gravity with the Stacked Phase Space around Galaxy Clusters

In general relativity, the average velocity field of dark matter around galaxy clusters is uniquely determined by the mass profile. The latter can be measured through weak lensing. We propose a new method of measuring the velocity field (phase space density) by stacking redshifts of surrounding galaxies from a spectroscopic sample. In combination with lensing, this yields a direct test of gravity on scales of 1–30 Mpc. Using N-body simulations, we show that this method can improve upon current constraints on f(R) and Dvali-Gabadadze-Porrati model parameters by several orders of magnitude when applied to upcoming imaging and redshift surveys.