# 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{sup 2} 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.

- Authors:

- School of Physics and Astronomy, University of Southampton, Highfield, Southampton, SO17 1BJ (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22375889

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCELERATION; CORRECTIONS; COSMOLOGICAL INFLATION; COSMOLOGY; FLUCTUATIONS; GRAVITATION; NONLINEAR PROBLEMS; NONLUMINOUS MATTER; POTENTIALS; SCALARS; TENSORS; UNIVERSE; WAVELENGTHS

### Citation Formats

```
Preston, Anthony W.H., and Morris, Tim R., E-mail: awhp1g12@soton.ac.uk, E-mail: T.R.Morris@soton.ac.uk.
```*Cosmological back-reaction in modified gravity and its implications for dark energy*. United States: N. p., 2014.
Web. doi:10.1088/1475-7516/2014/09/017.

```
Preston, Anthony W.H., & Morris, Tim R., E-mail: awhp1g12@soton.ac.uk, E-mail: T.R.Morris@soton.ac.uk.
```*Cosmological back-reaction in modified gravity and its implications for dark energy*. United States. doi:10.1088/1475-7516/2014/09/017.

```
Preston, Anthony W.H., and Morris, Tim R., E-mail: awhp1g12@soton.ac.uk, E-mail: T.R.Morris@soton.ac.uk. Mon .
"Cosmological back-reaction in modified gravity and its implications for dark energy". United States. doi:10.1088/1475-7516/2014/09/017.
```

```
@article{osti_22375889,
```

title = {Cosmological back-reaction in modified gravity and its implications for dark energy},

author = {Preston, Anthony W.H. and Morris, Tim R., E-mail: awhp1g12@soton.ac.uk, E-mail: T.R.Morris@soton.ac.uk},

abstractNote = {We study the effective stress-energy tensor induced by cosmological inhomogeneity in f(R)=R+c R{sup 2} 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.},

doi = {10.1088/1475-7516/2014/09/017},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 09,

volume = 2014,

place = {United States},

year = {Mon Sep 01 00:00:00 EDT 2014},

month = {Mon Sep 01 00:00:00 EDT 2014}

}