Non-singular pre-big bang scenarios from all-order $\alpha'$ corrections

TL;DR

This paper reformulates string cosmology equations with all-order $mbda'$ corrections in Hamiltonian form, enabling the construction of non-singular pre-big bang scenarios that smoothly connect accelerated and decelerated phases.

Contribution

It provides a Hamiltonian formulation of $O(d,d)$-symmetric string cosmology equations at all orders in $mbda'$ and constructs non-singular pre-big bang models.

Findings

Constructed non-singular, non-perturbative pre-big bang solutions.

These solutions interpolate smoothly between accelerated and decelerated phases.

Solutions include a brief contraction phase around the bounce.

Abstract

We reformulate in Hamiltonian language the recent proposal by Hohm and Zwiebach of an action yielding the most general $O(d,d)$-symmetric string cosmology equations, at tree-level in the string-loop expansion, but to all orders in the $\alpha'$ expansion. This allows us to give a simple characterization of a large class of non-singular, non-perturbative, pre-big bang scenarios smoothly interpolating between a low-energy initial accelerated (string frame) expansion and a phase of final (string and Einstein frame) decelerated expansion. Interestingly, these solutions must necessarily include, just around the bounce, a very short phase of (string-frame) contraction.