Kantowski-Sachs String Cosmologies

TL;DR

This paper derives new exact solutions for string cosmologies with Kantowski-Sachs geometry, involving non-zero dilaton and axion fields, highlighting anisotropic models with space-dependent axion fields that do not isotropize.

Contribution

It introduces novel exact solutions to string equations with non-zero dilaton and axion fields in Kantowski-Sachs backgrounds, including cases with space-dependent axion fields.

Findings

Solutions include time-dependent dilaton and axion fields.

Space-dependent axion fields lead to anisotropic models.

Models do not isotropize due to distinguished spatial directions.

Abstract

We present new exact solutions of the low-energy-effective-action string equations with both dilaton $\phi $ and axion $H$ fields non-zero. The background universe is of Kantowski-Sachs type. We consider the possibility of a pseudoscalar axion field $h$ ($H=e^\phi (dh)^{*}$) that can be either time or space dependent. The case of time-dependent $h$ reduces to that of a stiff perfect-fluid cosmology. For space-dependent $h$ there is just one non-zero time-space-space component of the axion field $H$, and this corresponds to a distinguished direction in space which prevents the models from isotropising. Also, in the latter case, both the axion field $H$ and its tensor potential $B$ ($H=dB$) are dependent on time and space yet the energy-momentum tensor remains time-dependent as required by the homogeneity of the cosmological model.