Quasi‐local variables and scalar averaging in LTB dust models
Dec, 200910 pages
Part of Proceedings, International Conference on Invisible Universe : Paris, France, June 29-July 3, 2009, 1146-1155
Published in:
- AIP Conf.Proc. 1241 (2010) 1, 1146-1155
Contribution to:
- Published: Jun 28, 2010
e-Print:
- 0912.4074 [gr-qc]
DOI:
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Abstract: (AIP)
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 Qin 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.- 95.36.+x
- 02.30.Sa
- 98.80.Es
- 98.80.Cq
- cosmology
- Universe
- functional analysis
- dark matter
- Dark energy
- Spatial analysis
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