High frequency limit for gravitational perturbations of cosmological models in modified gravity theories

TL;DR

This paper demonstrates that in certain modified gravity theories, the effective gravitational stress-energy tensor for short-wavelength perturbations behaves like radiation, similar to general relativity, and does not mimic dark energy.

Contribution

It shows that in FLRW cosmological models within specific f(R) gravity theories, the stress-energy tensor remains radiation-like, extending known results from general relativity.

Findings

Effective stress-energy tensor is traceless and radiation-like in f(R) gravity.

Higher order derivatives do not produce dark energy effects in short-wavelength perturbations.

Results hold for scalar-tensor equivalents of f(R) gravity.

Abstract

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.