Non-singular pre-big bang scenarios from all-order ${\alpha }^{\prime }$ corrections

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 ${\alpha }^{\prime }$ 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.

18 pages, 10 figures. Final version published in JHEP 07 (2023) 144. Available at https://link.springer.com/article/10.1007/JHEP07(2023)144

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• Double Field Theory at Order ${\alpha }^{\prime }$
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• General String Cosmologies at Order ${\alpha }^{\prime }{}^3$
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• Large $D$ gravity and low $D$ string via ${\alpha }^{\prime }$ corrections
• Perturbations in $\mathbf{O}(D,D)$ string cosmology from double field theory
• Arrows of time in bouncing cosmologies
• A simple example of "non-minimal" Pre-Big Bang scenario