On the gauge invariance of the locally averaged Friedmann Universe and the Hubble tension

TL;DR

This paper investigates whether spatial averaging in inhomogeneous cosmology is gauge invariant, confirming its invariance within gauge-invariant perturbation theory, which impacts interpretations of the Hubble tension.

Contribution

It demonstrates the gauge invariance of spatial averaging in cosmology using gauge-invariant perturbation theory, clarifying its physical validity.

Findings

Spatial averaging is gauge invariant in cosmology.

The gauge invariance supports the physical relevance of local expansion rate variations.

Implications for resolving the Hubble tension are discussed.

Abstract

The Hubble tension cast a blight on the standard cosmology. As a possible attitude to the problem, the local variation of the expansion rate in an inhomogeneous cosmology has been proposed where the spatial averaging over a finite domain was introduced in order to construct local Friedmann spacetime. However, it is not clear that the concept of the spatial averaging itself is gauge invariant or not. Namely the conclusion obtained by the averaging in a particular gauge is physically meaningful or not. In this paper we address this question, namely the gauge invariance of the spatial averaging in cosmology . We show that the answer is positive by studying the spatial average in the gauge-invariant cosmological perturbation theory.