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

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.