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.
