Averaging in Spherically Symmetric Cosmology

TL;DR

This paper investigates how spatial averaging in spherically symmetric cosmological models affects Einstein's equations, revealing that inhomogeneities can mimic spatial curvature and influence cosmic acceleration.

Contribution

It provides a detailed calculation of the correlation tensor in spherically symmetric models, showing its role as an effective spatial curvature and its impact on cosmological dynamics.

Findings

Correlation tensor in FLRW models acts as spatial curvature.

Inhomogeneities can significantly affect cosmic acceleration.

Averaging in non-FLRW backgrounds introduces anisotropic fluid effects.

Abstract

In the macroscopic gravity 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 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 back-reaction) in an FLRW background, which support the main conclusions of the analysis.