Kalb-Ramond backgrounds in $\alpha'$-complete cosmology

TL;DR

This paper investigates the effects of all-order $\alpha'$ corrections on cosmological models with Kalb-Ramond fields within an O(d,d) duality invariant framework, revealing non-isotropic two-form solutions and their cosmological implications.

Contribution

It introduces a duality-invariant approach to include all $\alpha'$ corrections in matter-coupled cosmological equations with Kalb-Ramond fields, highlighting non-isotropic solutions.

Findings

Derived solutions for vacuum and matter cases.

Demonstrated non-isotropic nature of the Kalb-Ramond two-form.

Discussed Einstein frame cosmologies with $\alpha'$$ corrections.

Abstract

We study the matter-coupled equations of motion for cosmological NS massless fields including all $\alpha'$ corrections in an O$(d,d)$ duality invariant approach, with emphasis on the Kalb-Ramond two-form field $B_{(2)}$ and its source. Solutions for the vacuum and matter case are found and the corresponding Einstein frame cosmologies are discussed. We also show that the ansatz for $B_{(2)}$ required by the duality invariant framework implies that the two-form is non-isotropic.