Quasi-local variables and scalar averaging in LTB dust models

TL;DR

This paper introduces quasi-local scalar variables in LTB models to analyze back-reaction effects, demonstrating conditions under which these effects can mimic dark energy and providing rigorous proofs of positivity in certain curvature scenarios.

Contribution

It defines quasi-local scalars as functionals in LTB models and links them to Buchert's averaging, offering rigorous proofs of back-reaction positivity and potential dark energy mimicking.

Findings

Back-reaction is positive in models with negative or asymptotically negative curvature.

Models with positive curvature decaying to zero can exhibit effective acceleration.

Quasi-local scalars generalize proper volume averages and connect to back-reaction analysis.

Abstract

We introduce quasi--local (QL) scalar variables in spherically symmetric LTB models. If the QL scalars are defined as functionals, they become weighed averages that generalize the standard proper volume averages on space slices orthogonal to the 4-velocity. We examine the connection between QL functions and functionals and the "back-reaction" term $Q$ in the context of Buchert's scalar averaging formalism. With the help of the QL scalars we provide rigorous proof that back--reaction is positive for (i) all LTB models with negative and asymptotically negative spatial curvature, and (ii) models with positive curvature decaying to zero asymptotically in the radial direction. We show by means of qualitative, but robust, arguments that generic LTB models exist, either with clump or void profiles, for which an "effective" acceleration associated with Buchert's formalism can mimic the effects of dark energy.