%0 Journal Article
%T Cosmological back-reaction in modified gravity and its implications for dark energy
%A Anthony W. H. Preston
%A Tim R. Morris
%J Physics
%D 2014
%I arXiv
%R 10.1088/1475-7516/2014/09/017
%X We study the effective stress-energy tensor induced by cosmological inhomogeneity in $f(R)=R+cR^2$ and equivalent scalar-tensor theories, motivated both by models of early universe inflation and by phenomenological alternative cosmologies to the standard $\Lambda$-CDM. We use Green and Wald's framework for averaging over classical fluctuations of short-wavelength $\lambda$. By ensuring that the leading non-linear terms from the fluctuations of the Einstein terms and the corrections both contribute in the formal limit as $\lambda\to0$, we derive a diffeomorphism invariant effective stress-energy tensor whose trace is non-vanishing and of the right sign to potentially account for the current acceleration of the universe. However a more phenomenologically acceptable dark energy model would be required if this effect were to fully account for the current acceleration.
%U http://arxiv.org/abs/1406.5398v2