Gravitational Effects of Disformal Couplings

We consider how a nearly massless scalar field conformally and disformally coupled to matter can affect the dynamics of gravitationally interacting bodies. We focus on the case of two interacting objects and we obtain the effective metric driving the dynamics of the two body system when reduced to one body in the centre of mass frame. We then concentrate on the case of a light particle in the scalar and gravitational fields generated by a heavy object and find the effects of the conformal and disformal couplings on the body's trajectory such as the advance of perihelion and the Shapiro time delay. The disformal coupling leads to a negligible contribution to the Shapiro effect and therefore no constraint from the Cassini experiment. On the other hand, it contributes to the perihelion advance leading to a weak bound on the strength of the disformal coupling itself. Finally, we remark that the disformal coupling gives rise to a contribution to the perihelion advance which varies quadratically with the mass of the heavy body, leading to possible strong effects for stars in the vicinity of astrophysical black holes. For neutron stars in a binary system, the disformal effects vary as the quartic power of the size of the orbit which might lead to interesting consequences in the inspiralling phase prior to a merger.