Cosmological back-reaction in modified gravity and its implications for dark energy

Abstract

We study the effective stress-energy tensor induced by cosmological inhomogeneity in f(R)=R+c R2 and equivalent scalar-tensor theories, motivated both by models of early universe inflation and by phenomenological alternative cosmologies to the standard Λ-CDM. We use Green and Wald's framework for averaging over classical fluctuations of short-wavelength λ. 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 λ→0, 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.