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

TL;DR

This paper investigates how small-scale inhomogeneities in modified gravity theories, specifically $f(R)=R+cR^2$, can produce an effective stress-energy tensor that might explain the universe's accelerated expansion, though more work is needed for a complete dark energy model.

Contribution

It derives a diffeomorphism invariant effective stress-energy tensor in $f(R)$ gravity considering inhomogeneities, highlighting its potential role in cosmic acceleration.

Findings

Effective stress-energy tensor has a non-zero trace compatible with acceleration.

Inhomogeneities in $f(R)$ gravity can mimic dark energy effects.

Further development needed for a phenomenologically viable dark energy explanation.

Abstract

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.