Construct α′ 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 α ′ expansion. When higher order α ′ 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 α ′ corrected EOM and loop corrected EOM. This map enables us to easily generate a loop corrected solution from an α ′ corrected solution, and vice versa, therefore substantially enlarges the solution space.

Cosmology at the top of the α′ tower

“…section 2.3), only the trivial Minkowski solution is obtainable, i.e., H ≡ 0 andḢ ≡ 0; a string-frame bounce is certainly not achievable if p = 0. This is in tension with the results from [102,103], where non-singular bouncing solutions had been obtained 20 in the absence of any matter sector.…”

“…The issue with the solutions found in[102,103] appears to be that at the point in time where H = 0 andḢ > 0, one does not recover F (H) = 0 as one should. This is due to a problem when inverting the solution for H(t) to find time in terms of H: the inversion is ill defined at the point H = 0, hence the solution cannot continuously hold through H = 0.…”

The generalized Bergshoeff-de Roo identification. Part II

“…• Our results can contribute to many recent works that study the role of T-duality for higher derivatives in the context of black-holes [67][68][69][70][71] and other solutions of cosmological relevance [65,66,[72][73][74][75][76][77][78].…”

Cosmological α′-corrections from the functional renormalization group

“…The resulting mini-superspace effective actions involve a single function of the Hubble parameter, whose perturbative expansion ought to match the α expansion order by order. Recent works have investigated some phenomenological aspects of effective actions of this type [33][34][35][36]. This remarkable result provides our starting point: combining the consistency constraints of string theory with FRG methods can potentially shed light on string theory at large curvature.…”