Duality Invariance of Cosmological Solutions with Torsion

TL;DR

This paper investigates how duality transformations affect cosmological solutions with torsion, demonstrating conditions under which maximal symmetry can be preserved in string-inspired backgrounds.

Contribution

It introduces a framework for understanding the invariance of generalized maximal symmetry under duality transformations in torsion-inclusive cosmological models.

Findings

Duality transformations can produce inequivalent solutions that are not maximally symmetric.

Maximal symmetry can be preserved with torsion under specific conditions.

The results are relevant for string-inspired cosmological backgrounds.

Abstract

We show that for a string moving in a background consisting of maximally symmetric gravity, dilaton field and second rank antisymmetric tensor field, the $O(d) \otimes O(d)$ transformation on the vacuum solutions gives inequivalent solutions that are not maximally symmetric. We then show that the usual physical meaning of maximal symmetry can be made to remain unaltered even if torsion is present and illustrate this through two toy models by determining the torsion fields, the metric and Killing vectors. Finally we show that under the $O(d) \otimes O(d)$ transformation this generalised maximal symmetry can be preserved under certain conditions. This is interesting in the context of string related cosmological backgrounds.