Anisotropic Born-Infeld Cosmologies

TL;DR

This paper constructs anisotropic cosmological models from Einstein's equations coupled with nonlinear electrodynamics, exploring their properties and late-time isotropization.

Contribution

It introduces new anisotropic cosmological solutions by interchanging space and time roles in spherically symmetric Einstein-nonlinear electrodynamics models.

Findings

Constant time hypersurfaces have topology R×S^2

The radius of the 2-sphere vanishes as t approaches zero

At late times, the universe appears homogeneous and isotropic

Abstract

Anisotropic cosmological spacetimes are constructed from spherically symmetric solutions to Einstein's equations coupled to nonlinear electrodynamics and a positive cosmological constant. This is accomplished by finding solutions in which the roles of $r$ and $t$ are interchanged for all $r>0$ (i.e. $r$ becomes timelike and $t$ becomes spacelike). Constant time hypersurfaces have topology $R\times S^2$ and in all the spacetimes considered the radius of the two sphere vanishes as $t$ goes to zero. The scale factor of the other dimension diverges as $t$ goes to zero in some solutions and vanishes (or goes to a constant) in other solutions. At late times local observers would see the universe to be homogeneous and isotropic.