From the String Vacuum to FLRW or De Sitter Via $α'$ Corrections

We first make more precise a recent "Hamiltonian" reformulation of the Hohm-Zwiebach approach to the tree-level, O(d, d)-invariant string cosmology equations at all orders in the symbolscript expansion, and recall how it allows to give a simple characterization of a large class of cosmological scenarios connecting, through a non-singular bounce, two duality-related per-turbative solutions at early and late times. We then discuss the effects of adding to the action a non-perturbative, O(d, d)-breaking, dilaton potential V (phi). The resulting cosmological so-lutions, assumed to approach at early times the perturbative string vacuum (with vanishing curvature and string coupling), can stabilize the dilaton at late times and simultaneously approach either a matter-dominated FLRW cosmology or a de-Sitter-like inflationary phase, depending on initial conditions and on the properties of V (phi) at moderate-coupling. We also identify a general mechanism for generating isotropic late-time attractors from a large basin of anisotropic initial conditions.