Magneto-dilatonic Bianchi-I cosmology: isotropization and singularity problems

Abstract

We study the evolution of Bianchi-I space-times filled with a global unidirectional electromagnetic field $F_{mn}$ interacting with a massless scalar dilatonic field according to the law Ψ(ϕ) F^{mn} F_{mn} where Ψ(ϕ) > 0 is an arbitrary function. A qualitative study, among other results, shows that (i) the volume factor always evolves monotonically, (ii) there exist models becoming isotropic at late times and (iii) the expansion generically starts from a singularity but there can be special models starting from a Killing horizon preceded by a static stage. All these features are confirmed for exact solutions found for the usually considered case Ψ= e^{2λϕ}, λ= const. In particular, isotropizing models are found for |λ| > 1/\sqrt{3}. In the special case |λ| = 1, which corresponds to models of string origin, the string metric behaviour is studied and shown to be qualitatively similar to that of the Einstein frame metric.

arXiv commentLatex2e, 10 pages

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