On average properties of inhomogeneous fluids in general relativity I: dust cosmologies

TL;DR

This paper derives generalized Friedmann equations for inhomogeneous dust cosmologies in general relativity, incorporating backreaction effects of inhomogeneities on average cosmic expansion, and explores their implications for structure formation.

Contribution

It introduces a new set of equations accounting for backreaction in inhomogeneous cosmologies, extending standard Friedmann models to include effects of inhomogeneities.

Findings

Backreaction influences average curvature during structure formation.

Universal relation between backreaction and scalar curvature is established.

Effective expansion law derived for specific curvature conditions.

Abstract

For general relativistic spacetimes filled with irrotational `dust' a generalized form of Friedmann's equations for an `effective' expansion factor $a_D (t)$ of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new equations include the `backreaction effect' of inhomogeneities on the average expansion of the model. A universal relation between `backreaction' and average scalar curvature is also given. For cosmologies whose averaged spatial scalar curvature is proportional to $a_D^{-2}$, the expansion law governing a generic domain can be found. However, as the general equations show, `backreaction' acts as to produce average curvature in the course of structure formation, even when starting with space sections that are spatially flat on average.