Backreaction in the Lemaitre-Tolman-Bondi model

TL;DR

This paper analytically investigates backreaction effects in the Lemaître-Tolman-Bondi model, revealing how different measurement hypersurfaces influence the perceived impact on cosmic expansion.

Contribution

It provides an analytical study of backreaction in the Lemaître-Tolman-Bondi model, comparing effects on different hypersurfaces and their influence on the Hubble law.

Findings

Backreaction slows expansion when measured with proper time.

Backreaction speeds up expansion when measured with energy density.

Different hypersurface choices lead to contrasting backreaction effects.

Abstract

We study backreaction analytically using the parabolic Lemaitre-Tolman-Bondi universe as a toy model. We calculate the average expansion rate and energy density on two different hypersurfaces and compare the results. We also consider the Hubble law and find that backreaction slows down the expansion if measured with proper time, but speeds it up if measured with energy density.