Equivalence Principle on Cosmological Backgrounds in Scalar-Tensor
  Theories
  We study the extent up to which the equivalence principle is obeyed in models
of modified gravity and dark energy involving a single scalar degree of
freedom. We focus on the effective field theories of dark energy describing the
late time acceleration in the presence of ordinary matter species. In their
covariant form these coincide with the Horndeski theories on a cosmological
background with a slowly varying Hubble rate and a time-dependent scalar field.
We show that in the case of an exactly de Sitter universe both the weak and
strong equivalence principles hold. This occurs due to the combination of the
shift symmetry of the scalar and the time translational invariance of de Sitter
space. When generalized to Friedmann--Robertson--Walker cosmologies (FRW) we
show that the weak equivalence principle is obeyed for test particles and
extended objects in the quasi-static subhorizon limit. We do this by studying
the field created by an extended object moving in an FRW background as well as
its equation of motion in an external gravitational field. We also estimate the
corrections to the geodesic equation of the extended object due to the
approximations made.
