The Hubble rate in averaged cosmology

TL;DR

This paper investigates how different definitions of the averaged Hubble rate in perturbed cosmology affect the measured value and variance of the Hubble constant, highlighting small corrections and intrinsic measurement uncertainties.

Contribution

It introduces a gauge-invariant definition of the averaged Hubble rate and compares various existing definitions through second-order perturbation theory calculations.

Findings

Small corrections to the background Hubble rate due to averaging.

Intrinsic variance in H_0 related to measurement scale.

Differences in definitions significantly impact the measured Hubble rate.

Abstract

The calculation of the averaged Hubble expansion rate in an averaged perturbed Friedmann-Lemaitre-Robertson-Walker cosmology leads to small corrections to the background value of the expansion rate, which could be important for measuring the Hubble constant from local observations. It also predicts an intrinsic variance associated with the finite scale of any measurement of H_0, the Hubble rate today. Both the mean Hubble rate and its variance depend on both the definition of the Hubble rate and the spatial surface on which the average is performed. We quantitatively study different definitions of the averaged Hubble rate encountered in the literature by consistently calculating the backreaction effect at second order in perturbation theory, and compare the results. We employ for the first time a recently developed gauge-invariant definition of an averaged scalar. We also discuss the variance of the Hubble rate for the different definitions.