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Departamento de Gravitación y Teoría de CamposSeminarios 2012 |
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Instituto de Ciencias Nucleares, UNAM |
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Departamento de Gravitación y Teoría de CamposSeminarios 2012 |
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Instituto de Ciencias Nucleares, UNAM |
Jueves 14 de febrero, a las 17:00 hrs en la Sala de Seminarios del ICN
Roberto Sussman (ICN, UNAM)
Scalar averaging over inhomogeneous cosmological models
| I provide a quick summary of the averaging problem in GR, followed by a description of the proper volume scalar averaging scheme derived by Buchert in a 1+3 covariant framework. The latter scheme leads to averaged dynamical equations containing correlation terms (the so called "back-reaction") that can (at least in principle) mimic the effects of a cosmological constant. I present in more detail the alternative approach of a proper volume average with a non-trivial weight factor. For two of the most important classes of inhomogeneous cosmologies (LTB and Szekeres models), the weighed average leads to a fully determined system of evolution equations for the averaged covariant scalars and their fluctuations and perturbations. While these evolution equations lack the "back-reaction" terms, they allow for a deeper coordinate independent theoretical understanding of the deviation from FLRW homogeneity, either in terms of a rigorous formalism of exact perturbations over an FLRW abstract background, or through a definition of gravitational entropy in a phase space made by weighed averages of the density and Hubble scalar velocity. I conclude by providing a quick outline on how this weighed scalar averaging can be applied to more general geometries and to various theoretically relevant issues in GR, such as: a rigorous approach to gravitational fluctuations and perturbations and a practical definition of gravitational entropy. |
