# Averaging in spherically symmetric cosmology

## Abstract

The averaging problem in cosmology is of fundamental importance. When applied to study cosmological evolution, the theory of macroscopic gravity (MG) can be regarded as a long-distance modification of general relativity. In the MG approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We study the averaging problem within the class of spherically symmetric cosmological models. That is, we shall take the microscopic equations and effect the averaging procedure to determine the precise form of the correlation tensor in this case. In particular, by working in volume-preserving coordinates, we calculate the form of the correlation tensor under some reasonable assumptions on the form for the inhomogeneous gravitational field and matter distribution. We find that the correlation tensor in a Friedmann-Lemaitre-Robertson-Walker (FLRW) background must be of the form of a spatial curvature. Inhomogeneities and spatial averaging, through this spatial curvature correction term, can have a very significant dynamical effect on the dynamics of the Universe and cosmological observations; in particular, we discuss whether spatial averaging might lead to a more conservative explanation of the observed acceleration of the Universe (without the introduction of exotic dark matter fields). We alsomore »

- Authors:

- Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia (Canada)

- Publication Date:

- OSTI Identifier:
- 21011049

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.043506; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACCELERATION; ANISOTROPY; CORRECTIONS; CORRELATIONS; COSMOLOGICAL MODELS; COSMOLOGY; DISTURBANCES; EINSTEIN FIELD EQUATIONS; GENERAL RELATIVITY THEORY; GRAVITATION; GRAVITATIONAL FIELDS; MATHEMATICAL SOLUTIONS; NONLUMINOUS MATTER; TENSORS; UNIVERSE

### Citation Formats

```
Coley, A. A., and Pelavas, N.
```*Averaging in spherically symmetric cosmology*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.043506.

```
Coley, A. A., & Pelavas, N.
```*Averaging in spherically symmetric cosmology*. United States. doi:10.1103/PHYSREVD.75.043506.

```
Coley, A. A., and Pelavas, N. Thu .
"Averaging in spherically symmetric cosmology". United States.
doi:10.1103/PHYSREVD.75.043506.
```

```
@article{osti_21011049,
```

title = {Averaging in spherically symmetric cosmology},

author = {Coley, A. A. and Pelavas, N.},

abstractNote = {The averaging problem in cosmology is of fundamental importance. When applied to study cosmological evolution, the theory of macroscopic gravity (MG) can be regarded as a long-distance modification of general relativity. In the MG approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We study the averaging problem within the class of spherically symmetric cosmological models. That is, we shall take the microscopic equations and effect the averaging procedure to determine the precise form of the correlation tensor in this case. In particular, by working in volume-preserving coordinates, we calculate the form of the correlation tensor under some reasonable assumptions on the form for the inhomogeneous gravitational field and matter distribution. We find that the correlation tensor in a Friedmann-Lemaitre-Robertson-Walker (FLRW) background must be of the form of a spatial curvature. Inhomogeneities and spatial averaging, through this spatial curvature correction term, can have a very significant dynamical effect on the dynamics of the Universe and cosmological observations; in particular, we discuss whether spatial averaging might lead to a more conservative explanation of the observed acceleration of the Universe (without the introduction of exotic dark matter fields). We also find that the correlation tensor for a non-FLRW background can be interpreted as the sum of a spatial curvature and an anisotropic fluid. This may lead to interesting effects of averaging on astrophysical scales. We also discuss the results of averaging an inhomogeneous Lemaitre-Tolman-Bondi solution as well as calculations of linear perturbations (that is, the backreaction) in an FLRW background, which support the main conclusions of the analysis.},

doi = {10.1103/PHYSREVD.75.043506},

journal = {Physical Review. D, Particles Fields},

number = 4,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}