Example of an inhomogeneous cosmological model in the context of backreaction

TL;DR

This paper presents an inhomogeneous cosmological model based on linear perturbation theory, combining Einstein-de Sitter background with dust overdensities, and compares different averaging schemes' effects on angular diameter distances.

Contribution

It introduces a new inhomogeneous cosmological model that allows simultaneous application of Green-Wald and Buchert averaging methods, facilitating comparison of their predictions.

Findings

The model successfully integrates Green-Wald and Buchert averaging schemes.

Angular diameter distances differ between the inhomogeneous model and averaged space-times.

Comparison highlights the impact of inhomogeneities on cosmological distance measures.

Abstract

In this article, we present an example of an inhomogeneous cosmological model, which is inspired by the linear perturbation theory. The metric of this model can be described as the Einstein-de Sitter background with a periodically distributed dust overdensities. The model construction enables application of the Green-Wald averaging scheme and the Buchert averaging technique simultaneously. We compare the angular diameter distance function of the considered model to the angular diameter distances corresponding to the average space-times given by the Green-Wald and the Buchert frameworks respectively.