O$(d,d)$ covariant String Cosmology to all orders in $\alpha^{\prime}$

TL;DR

This paper extends string cosmology models by incorporating all-order $\alpha'$ corrections in an O$(d,d)$ covariant framework, including matter sources, and explores de Sitter solutions.

Contribution

It introduces a covariant method to include matter sources in all-order $\alpha'$ corrected string cosmology equations, unifying different approaches.

Findings

Consistent equations for string cosmology with matter sources to all orders in $\alpha'$.

Demonstrates equivalence of different formulations of the corrected equations.

Discusses existence of perturbative and non-perturbative de Sitter solutions.

Abstract

Recently, all duality invariant $\alpha'$-corrections to the massless NS-NS sector of string theory on time-dependent backgrounds were classified and the form of their contribution to the action were calculated. In this paper we introduce matter sources in the resulting equations of motion in an O$(d,d)$ covariant way. We show that either starting with the corrected equations and sourcing them with matter or considering corrections to the matter sourced lowest order equations give the same set of equations that defines string cosmology to all orders in $\alpha'$. We also discuss perturbative and non-perturbative de Sitter solutions including matter.