Generalized Kasner Cosmologies with Induced Matter

Physics

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Scientific paper

We extend Paul Wesson's five dimensional induced matter model, which has previously been applied to a variety of isotropic cases, to a generalization of Kasner's anisotropic (Bianchi-type-I) cosmology. Wesson's model is a Kaluza-Klein approach in which assumptions of compactness are relaxed for the fifth coordinate, leading to extra "induced matter" terms in the stress-energy tensor. In similar spirit, we construct a five dimensional metric in which the spatial slices possess Bianchi-type-I geometry. We supplement the fourth time coordinate, t, with a fifth coordinate, ψ. We assume that each of the scale factors are dependent on both t and ψ. (This extends the work of Soccorro, Villanueva, and Pimental, who solved a related problem with only time dependence.) We find a set of solutions for the five dimensional Einstein equations, and determine the pressure and density of induced matter. We show that the assumption of positive density leads to the contraction over time of the fifth scale factor. Finally, employing our model, we speculate about a possible mechanism for the isotropization of the early universe.

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