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 $f(R)=R+c{R}^2$ 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 $\lambda \to 0$, 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.

arXiv comment23 pages, references updated, some arguments clarified

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Cited by in corpus (8)

• Manifestly diffeomorphism invariant classical Exact Renormalization Group
• Cosmology in Poincare gauge gravity with a pseudoscalar torsion
• Quantum Corrections to the Gravitational Backreaction
• Cosmic backreaction and Gauss's law
• Cosmological backreaction in higher-derivative gravity expansions
• Gravitational wave energy momentum-tensor in reduced Horndeski theories
• Translational Symmetry Breaking in Higgs & Gauge Theory, and the Cosmological Constant
• On energy-momentum tensor for gravitational waves in $f(R)$ gravity