de Sitter, ${\alpha }^{\prime }$-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 ${\alpha }^{\prime }$ 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.

v2: minor improvements, references. v3: wording improved in some places, minor clarifications. JCAP version, but with an additional acknowledgment

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Cited by in corpus (18)

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• Duality-invariant extensions of Einstein-Maxwell theory
• Construct ${\alpha }^{\prime }$ corrected or loop corrected solutions without curvature singularities
• Cosmology at the top of the ${\alpha }^{\prime }$ tower
• The generalized Bergshoeff-de Roo identification II
• Contracting Cosmologies and the Swampland
• Kalb-Ramond backgrounds in ${\alpha }^{\prime }$-complete cosmology
• Small free field inflation in higher curvature gravity
• Non-linear stability of ${\alpha }^{\prime }$-corrected Friedmann equations
• Stability of the non-perturbative $O(D,D)$ de-Sitter spacetime. The isotropic case
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Supersymmetry breaking, brane dynamics and Swampland conjectures
• Two non-perturbative ${\alpha }^{\prime }$ corrected or loop corrected string cosmological solutions
• Duality covariant field redefinitions