Back-reaction and effective acceleration in generic LTB dust models

Abstract

We provide a thorough examination of the conditions for the existence of\nback-reaction and an "effective" acceleration (in the context of Buchert's\naveraging formalism) in regular generic spherically symmetric\nLemaitre-Tolman-Bondi (LTB) dust models. By considering arbitrary spherical\ncomoving domains, we verify rigorously the fulfillment of these conditions\nexpressed in terms of suitable scalar variables that are evaluated at the\nboundary of every domain. Effective deceleration necessarily occurs in all\ndomains in: (a) the asymptotic radial range of models converging to a FLRW\nbackground, (b) the asymptotic time range of non-vacuum hyperbolic models, (c)\nLTB self-similar solutions and (d) near a simultaneous big bang. Accelerating\ndomains are proven to exist in the following scenarios: (i) central vacuum\nregions, (ii) central (non-vacuum) density voids, (iii) the intermediate radial\nrange of models converging to a FLRW background, (iv) the asymptotic radial\nrange of models converging to a Minkowski vacuum and (v) domains near and/or\nintersecting a non-simultaneous big bang. All these scenarios occur in\nhyperbolic models with negative averaged and local spatial curvature, though\nscenarios (iv) and (v) are also possible in low density regions of a class of\nelliptic models in which local spatial curvature is negative but its average is\npositive. Rough numerical estimates between -0.003 and -0.5 were found for the\neffective deceleration parameter. While the existence of accelerating domains\ncannot be ruled out in models converging to an Einstein de Sitter background\nand in domains undergoing gravitational collapse, the conditions for this are\nvery restrictive. The results obtained may provide important theoretical clues\non the effects of back-reaction and averaging in more general non-spherical\nmodels.\n