Cosmological backreaction and its dependence on spacetime foliation

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.

arXiv comment9 pages, Letter, matches published version in CQG

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• An Almost-FLRW Universe as the Averaged Geometry in Macroscopic Gravity
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• Constraints on AvERA Cosmologies from Cosmic Chronometers and Type Ia Supernovae
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