High frequency limit for gravitational perturbations of cosmological
  models in modified gravity theories
  In general relativity, it has been shown that the effective gravitational
stress-energy tensor for short-wavelength metric perturbations acts just like
that for a radiation fluid, and thus, in particular, cannot provide any effects
that mimic dark energy. However, it is far from obvious if this property of the
effective gravitational stress-energy tensor is a specific nature held only in
the Einstein gravity, or holds also in other theories of gravity. In
particular, when considering modified gravity theories that involve higher
order derivative terms, one may expect to have some non-negligible effects
arising from higher order derivatives of short-wavelength perturbations. In
this paper, we argue this is not the case at least in the cosmological context.
We show that when the background, or coarse-grained metric averaged over
several wavelengths has FLRW symmetry, the effective gravitational
stress-energy tensor for metric perturbations of a cosmological model in a
simple class of f(R) gravity theories, as well as that obtained in the
corresponding scalar-tensor theory, takes a similar form to that in general
relativity and is in fact traceless, hence acting again like a radiation fluid.
