An $\alpha'$-complete theory of cosmology and its tensionless limit

We explore the exactly duality invariant higher-derivative extension of double field theory due to Hohm, Siegel and Zwiebach (HSZ) specialized to cosmological backgrounds. Despite featuring a finite number of derivatives in its original formulation, this theory encodes infinitely many $\alpha'$ corrections for metric, B-field and dilaton, which are obtained upon integrating out certain extra fields. We perform a cosmological reduction with fields depending only on time and show consistency of this truncation. We compute the $\alpha'^4$ coefficients of the general cosmological classification. As a possible model for how to deal with all $\alpha'$ corrections in string theory we give a two-derivative reformulation in which the extra fields are kept. The corresponding Friedmann equations are then ordinary second order differential equations that capture all $\alpha'$ corrections. We explore the tensionless limit $\alpha'\rightarrow \infty$, which features string frame de Sitter vacua, and we set up perturbation theory in $\frac{1}{\alpha'}$.