Averaged Lema\^itre-Tolman-Bondi dynamics

TL;DR

This paper presents an exactly solvable Lemaître-Tolman-Bondi model to analyze cosmological backreaction effects within Buchert's averaging formalism, explicitly linking inhomogeneities to average curvature and backreaction.

Contribution

It introduces a simple, explicit LTB-based solution to Buchert's equations, connecting inhomogeneous cosmological dynamics to average quantities in a novel way.

Findings

Derived volume Hubble rate in terms of scale factor

Explicitly determined fractional densities of curvature and backreaction

Provided a solvable toy model illustrating backreaction effects

Abstract

We consider cosmological backreaction effects in Buchert's averaging formalism on the basis of an explicit solution of the Lema\^itre-Tolman-Bondi (LTB) dynamics which is linear in the LTB curvature parameter and has an inhomogeneous bang time. The volume Hubble rate is found in terms of the volume scale factor which represents a derivation of the simplest phenomenological solution of Buchert's equations in which the fractional densities corresponding to average curvature and kinematic backreaction are explicitly determined by the parameters of the underlying LTB solution at the boundary of the averaging volume. This configuration represents an exactly solvable toy model but it does not adequately describe our "real" Universe.