Equivalence principle violation in weakly Vainshtein-screened systems

Massive gravity, Galileon and braneworld models that modify gravity to explain cosmic acceleration utilize the nonlinear field interactions of the Vainshtein mechanism to screen fifth forces in high density regimes. These source-dependent interactions cause apparent equivalence principle violations. In the weakly screened regime violations can be especially prominent since the fifth forces are at near full strength. Since they can also be calculated perturbatively, we derive analytic solutions for the cubic Galileon: the motion of massive objects in compensated shells and voids and infall toward halos that are spherically symmetric. Using numerical techniques we show that these solutions are valid until the characteristic scale becomes comparable to the Vainshtein radius. We find a relative acceleration of more massive objects toward the center of a void and a reduction of the infall acceleration that increases with the mass ratio of the halos which can in principle be used to test the Vainshtein screening mechanism.