Duality invariant cosmology to all orders in α'

While the classification of alpha' corrections of string inspired effective theories remains an unsolved problem, we show how to classify duality invariant alpha' corrections for purely time-dependent (cosmological) backgrounds. We determine the most general duality invariant theory to all orders in alpha' 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'. We construct nonperturbative solutions and display duality invariant theories featuring string-frame de Sitter vacua.