Equivalence principle violation in nonminimally coupled gravity and constraints from lunar laser ranging

We analyze the dynamics of the Sun-Earth-Moon system in the context of a particular class of theories of gravity where curvature and matter are nonminimally coupled. These theories can potentially violate the equivalence principle as they give origin to a fifth force and a extra non-Newtonian force that may imply that Earth and Moon fall differently towards the Sun. We show, through a detailed analysis, that consistency with the bound on weak equivalence principle arising from 48 years of lunar laser ranging data, for a range of parameters of the nonminimally coupled gravity theory, can be achieved via the implementation of a suitable screening mechanism.