While the classification of ${\alpha }^{\prime }$ corrections of string inspired effective theories remains an unsolved problem, we show how to classify duality invariant ${\alpha }^{\prime }$ corrections for purely time-dependent (cosmological) backgrounds. We determine the most general duality invariant theory to all orders in ${\alpha }^{\prime }$ for the metric, $b$-field, and dilaton. The resulting Friedmann equations are studied when the spatial metric is a time-dependent scale factor times the Euclidean metric and the $b$-field vanishes. These equations can be integrated perturbatively to any order in ${\alpha }^{\prime }$. We construct nonperturbative solutions and display duality invariant theories featuring string-frame de Sitter vacua.

• Received 14 June 2019

DOI:https://doi.org/10.1103/PhysRevD.100.126011

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Published by the American Physical Society