Cosmological backreaction and its dependence on spacetime foliation

TL;DR

This paper introduces a coordinate-independent averaging formalism for scalar Einstein equations in cosmology, analyzing how spacetime foliation affects backreaction and proposing a new set of averaged equations with a global cosmological time.

Contribution

It develops a novel, coordinate-independent averaging method for Einstein's equations applicable to general spacetime foliations in cosmology.

Findings

Foliation dependence on backreaction is weak in cosmological contexts.

New averaged equations incorporate a global cosmological time.

Formalism applies to arbitrary fluids with tilted flow in 3+1 spacetime splits.

Abstract

The subject of cosmological backreaction in General Relativity is often approached by coordinate-dependent and metric-based analyses. We present in this letter an averaging formalism for the scalar parts of Einstein's equations that is coordinate-independent and only functionally depends on a metric. This formalism is applicable to general 3+1 foliations of spacetime for an arbitrary fluid with tilted flow. We clarify the dependence on spacetime foliation and argue that this dependence is weak in cosmological settings. We also introduce a new set of averaged equations that feature a global cosmological time despite the generality of the setting, and we put the statistical nature of effective cosmologies into perspective.