Back-reaction and effective acceleration in generic LTB dust models

Abstract

Abstract. We provide a thorough examination of the conditions for the existence of back-reaction and an "effective" acceleration (in the context of Buchert's averaging formalism) in regular generic spherically symmetric Lemaître-Tolman-Bondi (LTB) dust models. By considering arbitrary spherical comoving domains, we verify rigorously the fulfillment of these conditions expressed in terms of suitable scalar variables that are evaluated at the domains' boundaries. Effective deceleration necessarily occurs in all domains in: (a) the asymptotic radial range of models converging to a FLRW background, (b) the asymptotic time range of non-vacuum hyperbolic models, (c) LTB self-similar solutions and (d) near a simultaneous big bang. Accelerating domains are proven to exist in the following scenarios: (i) central vacuum regions, (ii) central (non-vacuum) density voids, (iii) the intermediate radial range of models converging to a FLRW background, (iv) the asymptotic radial range of models converging to a Minkowski vacuum and (v) domains near and/or intersecting a non-simultaneous big bang. All these scenarios occur in hyperbolic models with negative averaged and local spatial curvature, though scenarios (iv) and (v) are also possible in low density regions of a class of elliptic models in which local spatial curvature is negative but its average is positive. Rough numerical estimates between −0.003 and −0.5 were found for the effective deceleration parameter. While the existence of accelerating domains cannot be ruled out in models converging to an Einstein de Sitter background and in domains undergoing gravitational collapse, the conditions for this are very restrictive. The results obtained may provide important theoretical clues on the effects of back-reaction and averaging in more general non-spherical models.

Ricci focusing, shearing, and the expansion rate in an almost homogeneous Universe

“…For relativists, we would argue that, to study the effect of inhomogeneities on observations, it is first important to understand how much inhomogeneities affect the evolution of the background model. Such a study should focus on ρ(z) and H(z), and especially on potential deviations from (22), as this has the biggest impact on the distanceredshift relation (see, for example, Fig. 7 for a few percent change in the case where ρ(z) ≁ (1+z) 3 (cf.…”

Averaged Lemaître–Tolman–Bondi dynamics

“…A comprehensive analysis has been performed in [38]. We start our analysis with the simplest case of vanishing curvature.…”

A toy cosmological model with dynamical backreaction

“…(17) and (18) to find R i (t S i ). The results allow to find the velocities of the observers (21) and all their derivatives with respect to the Schwarzchild coordinates.…”

“…The most studied averaging of the Lemaitre-Tolman-Bondi solution was recently summarized by Sussman. 17 The other exact but less symmetrical model that can be explicitly averaged is the quasispherical Szekeres solution. 18,19 Some illustrative examples of acceleration parameter calculations were considered by Bull and Clifton 5 including the spatially averaged acceleration for LTB and Kasner-EdS models.…”