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.

Comments: V2: 14 pages, minor corrections, a footnote added in sec. 1, published version