A Covariant Road to Spatial Averaging in Cosmology : Scalar Corrections to the Cosmological Equations

TL;DR

This paper demonstrates that covariant scalar corrections to cosmological equations, derived via Macroscopic Gravity, are gauge-invariant and consistent with Buchert's averaging, potentially impacting our understanding of dark energy.

Contribution

It applies Zalaletdinov's covariant formalism to derive gauge-invariant scalar corrections to cosmological equations, confirming their consistency with Buchert's averaging approach.

Findings

Scalar corrections are gauge-invariant and observable.

Corrections are structurally identical to Buchert's results.

Supports the viability of averaging methods in cosmology.

Abstract

A consistent approach to Cosmology requires an explicit averaging of the Einstein equations, to describe a homogeneous and isotropic geometry. Such an averaging will in general modify the Einstein equations. The averaging procedure due to Buchert has attracted considerable attention recently since it offers the tantalizing hope of explaining the phenomenon of dark energy through such corrections. This approach has been criticized, however, on the grounds that its effects may be gauge artifacts. We apply the fully covariant formalism of Zalaletdinov's Macroscopic Gravity and show that, after making some essential gauge choices, the Cosmological equations receive \emph{spacetime scalar} corrections which are therefore observable in principle, and further, that the broad structure of these corrections is \emph{identical} to those derived by Buchert.