Construct $\alpha^{\prime}$ corrected or loop corrected solutions without curvature singularities

TL;DR

This paper develops systematic methods to construct non-perturbative string cosmological solutions in the bosonic gravi-dilaton system that are free of curvature singularities, incorporating higher order $oldsymbol{ ext{ extalpha}}^{ ext{ extprime}}$ corrections and relating them to loop corrections.

Contribution

It introduces a framework to generate non-perturbative solutions without singularities, compatible with all orders of $ ext{ extalpha}^{ ext{ extprime}}$ corrections, and establishes a map between $ ext{ extalpha}^{ ext{ extprime}}$ and loop corrected equations of motion.

Findings

Constructed non-perturbative solutions free of curvature singularities.

Provided a method to incorporate higher order $ ext{ extalpha}^{ ext{ extprime}}$ corrections.

Established a map linking $ ext{ extalpha}^{ ext{ extprime}}$ corrected and loop corrected solutions.

Abstract

For the bosonic gravi-dilaton system, we provide systematical approaches to construct non-perturbative string cosmological solutions without curvature singularities, which can match the perturbative solution to any order in $\alpha^{\prime}$ expansion. When higher order $\alpha^{\prime}$ corrections are calculated, they can be straightforwardly plugged in to generate compatible non-perturbative evolutions without curvature singularities. We also give a (phenomenological) map between $\alpha^{\prime}$ corrected EOM and loop corrected EOM. This map enables us to easily generate a loop corrected solution from an $\alpha^{\prime}$ corrected solution, and vice versa, therefore substantially enlarges the solution space.