Exact solution to the averaging problem in cosmology

TL;DR

This paper derives an exact two-scale solution to Einstein's equations in an inhomogeneous universe, explaining cosmic acceleration without dark energy by considering gravitational energy gradients between different regions.

Contribution

It provides a novel exact solution for averaging inhomogeneous cosmologies, challenging the need for dark energy in explaining cosmic acceleration.

Findings

Replaces Friedmann solutions with a two-scale average model.

Explains apparent acceleration via gravitational energy gradients.

Matches observational data without exotic dark energy.

Abstract

The exact solution of a two-scale Buchert average of the Einstein equations is derived for an inhomogeneous universe which represents a close approximation to the observed universe. The two scales represent voids, and the bubble walls surrounding them within which clusters of galaxies are located. As described elsewhere [gr-qc/0702082], apparent cosmic acceleration can be recognised as a consequence of quasilocal gravitational energy gradients between observers in bound systems and the volume average position in freely expanding space. With this interpretation, the new solution presented here replaces the Friedmann solutions, in representing the average evolution of a matter-dominated universe without exotic dark energy, while being observationally viable.