String Cosmology with a Time-Dependent Antisymmetric Tensor Potential

TL;DR

This paper derives exact solutions for anisotropic string cosmologies with a time-dependent antisymmetric tensor potential, revealing constraints on scale factors and showing the universe tends to contract at late times.

Contribution

It introduces a class of exact Bianchi I solutions in string cosmology with a time-dependent antisymmetric tensor potential, highlighting new anisotropic dynamics.

Findings

Late-time universe is contracting in these models.

Constraints on scale factors due to axion field gradient.

Exact solutions for anisotropic string cosmologies.

Abstract

We present a class of exact solutions for homogeneous, anisotropic cosmologies in four dimensions derived from the low-energy string effective action including a homogeneous dilaton $\phi$ and antisymmetric tensor potential $B_{\mu\nu}$. Making this potential time-dependent produces an anisotropic energy-momentum tensor, and leads us to consider a Bianchi I cosmology. The solution for the axion field must then only be a linear function of one spatial coordinate. This in turn places an upper bound on the product of the two scale factors evolving perpendicular to the gradient of the axion field. The only late-time isotropic solution is then a {\em contracting} universe.