Volume Expansion of Swiss-Cheese Universe

TL;DR

This study uses an exact Swiss-Cheese universe model to analyze how inhomogeneities influence cosmic volume expansion, revealing that small fluctuations slow expansion and large inhomogeneities lead to varied outcomes.

Contribution

It provides an exact solution-based analysis of inhomogeneity effects on universe expansion, extending previous perturbation studies to non-linear regimes.

Findings

Inhomogeneities slow down volume expansion compared to Einstein-de Sitter universe.

Large inhomogeneities can cause the universe's volume to be arbitrarily smaller or larger than the background.

Volume expansion rate approaches background value asymptotically.

Abstract

In order to investigate the effect of inhomogeneities on the volume expansion of the universe, we study modified Swiss-Cheese universe model. Since this model is an exact solution of Einstein equations, we can get an insight into non-linear dynamics of inhomogeneous universe from it. We find that inhomogeneities make the volume expansion slower than that of the background Einstein-de Sitter universe when those can be regarded as small fluctuations in the background universe. This result is consistent with the previous studies based on the second order perturbation analysis. On the other hand, if the inhomogeneities can not be treated as small perturbations, the volume expansion of the universe depends on the type of fluctuations. Although the volume expansion rate approaches to the background value asymptotically, the volume itself can be finally arbitrarily smaller than the background one and can be larger than that of the background but there is an upper bound on it.