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arXiv · 0911.0667

Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models

Simone Calogero·J. Mark Heinzle
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Abstract

The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we consider spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields. The dynamics of models of Bianchi types I, II, and IX are completely described; the two most striking results are the following: (i) There exist matter models, compatible with the standard energy conditions, such that solutions of Bianchi type IX (closed cosmologies) need not necessarily recollapse; there is an open set of forever expanding solutions. (ii) Generic type IX solutions associated with a matter model like Vlasov matter exhibit oscillatory behavior toward the initial singularity. This behavior differs significantly from that of vacuum/perfect fluid cosmologies; hence "matter matters". Finally, we indicate that our methods can probably be extended to treat a number of open problems, in particular, the dynamics of Bianchi type VIII and Kantowski-Sachs solutions.

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Simone Calogero, J. Mark Heinzle. 2009-11-03. Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models. https://doi.org/10.1016/j.physd.2010.11.015

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