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

TL;DR

This paper investigates the evolution of Bianchi-I cosmological models with electromagnetic and dilaton fields, showing conditions for isotropization, singularity behavior, and special solutions relevant to string theory.

Contribution

It provides a qualitative analysis and exact solutions for magneto-dilatonic Bianchi-I cosmologies, highlighting conditions for isotropization and singularity avoidance.

Findings

Volume factor evolves monotonically.

Some models become isotropic at late times.

Expansion often starts from a singularity, with exceptions.

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 \Psi(\phi) F^{mn} F_{mn} where \Psi(\phi) > 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 \Psi = e^{2\lambda\phi}, \lambda = const. In particular, isotropizing models are found for |\lambda| > 1/\sqrt{3}. In the special case |\lambda| = 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.