Quasi-local variables and scalar averaging in LTB dust models

Details Quasi-local variables and scalar averaging in LTB dust models Quasi-local variables and scalar averaging in LTB dust models

2009-12-21

arxiv.org/abs/0912.4074v1

AIP Conf.Proc.1241:1146-1155,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Submitted contribution for the proceedings of the "Invisible Universe Internationale Confernce", Palais de L'UNESCO, Paris, Fr

Scientific paper

10.1063/1.3462612

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.

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