Gravitational entropy of cosmic expansion

We apply a recent proposal to define "gravitational entropy" to the expansion of cosmic voids within the framework of non-perturbative General Relativity. By considering CDM void configurations compatible with basic observational constraints, we show that this entropy grows from post-inflationary conditions towards a final asymptotic value in a late time fully non-linear regime described by the Lemaitre-Tolman-Bondi (LTB) dust models. A qualitatively analogous behavior occurs if we assume a positive cosmological constant consistent with a $\Lambda$-CDM background model. However, the $\Lambda$ term introduces a significant suppression of entropy growth with the terminal equilibrium value reached at a much faster rate.Comment: 5 Pages, 2 figures, AN style. Contribution to Proceedings of the Second Caribbean Symposium on Nuclear and Astroparticle Physics (STARS 2013), La Habana, Cuba, 5-9 May 201

Quasi-local variables and scalar averaging in LTB dust models

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.Comment: Submitted contribution for the proceedings of the "Invisible Universe Internationale Confernce", Palais de L'UNESCO, Paris, France, June 29-July 3, 2009. Jean-Michel ALIMI, editor. 10 pages, 2 figures. AIP macros: layoutstyle 8x11singl