de Sitter, α′-corrections & duality invariant cosmology

Abstract

Demanding O(d, d)-duality covariance, Hohm and Zwiebach have written down the action for the most general cosmology involving the metric, b-field and dilaton, to all orders in α in the string frame. Remarkably, for an FRW metric-dilaton ansatz the equations of motion turn out to be quite simple, except for the presence of an unknown function of a single variable. If this unknown function satisfies some simple properties, it allows de Sitter solutions in the string frame. In this note, we write down the Einstein frame analogues of these equations, and make some observations that make the system tractable. Perhaps surprisingly, we find that a necessary condition for de Sitter solutions to exist is that the unknown function must satisfy a certain second order non-linear ODE. The solutions of the ODE do not have a simple power series expansion compatible with the leading supergravity expectation. We discuss possible interpretations of this fact. After emphasizing that all (potential) string and Einstein frame de Sitter solutions have a running dilaton, we write down the most general cosmologies with a constant dilaton in string/Einstein frame: these have power law scale factors.

O(d, d) covariant string cosmology to all orders in α′

“…It was shown in [35,30] that under some assumptions on the function F (H) there are de Sitter solutions to the equations (21), and that we can construct perturbative solutions by solving the equations order by order 3 . Conditions for having a de Sitter solution in the Einstein frame were studied in [38]. Furthermore, in [39] Anti-de Sitter solutions for the bosonic case were explored, and in [40,41] non-singular solutions were discussed.…”

Construct α′ corrected or loop corrected solutions without curvature singularities

“…This remarkable result leads them to show that, in bosonic string theory, non-perturbative de-Sitter (dS) vacua are admitted by including complete α ′ corrections. In [21], the analogy in the Einstein frame is then discussed. In our recent work [22], we showed that similar stories occur for configurations depending on a single space coordinate, and non-perturbative Anti-de-Sitter (AdS) vacua are also allowed.…”

Non-singular string cosmology via α′ corrections

“…They subsequently proved that non-perturbative de-Sitter (dS) vacua are possible in bosonic string theory. The analogy in the Einstein frame is then studied in [24].…”