The influence of inhomogeneities on the large-scale expansion of the universe

TL;DR

This paper investigates how inhomogeneities in matter distribution influence the large-scale expansion of the universe, showing that growing inhomogeneities can accelerate cosmic expansion.

Contribution

It provides an analytical example demonstrating the impact of matter inhomogeneities on the universe's average expansion rate, extending beyond linear approximations.

Findings

Inhomogeneities can significantly affect the universe's expansion rate.

The average expansion accelerates as inhomogeneities grow.

A condition is derived to determine when inhomogeneities become influential.

Abstract

The evolution of an inhomogeneous universe composed entirely of matter is followed from an early, nearly uniform state until the time when the inhomogeneities have begun to grow large. The particular distribution of matter studied in this article is chosen to have a periodic variation in only one of the directions, which is simple enough to allow the behavior of the metric to be solved analytically, well beyond a linear approximation based on the initial smallness of the fluctuation. This example provides an illustration of a universe where the inhomogeneities can affect its average expansion rate; and its simplicity allows a condition to be derived that tells when their presence should begin to become important. Since the averages of the non-uniform parts of the metric and the matter density grow faster than their uniform parts, the average expansion rate accelerates with the advent of the era governed by the inhomogeneities.