New non-perturbative de Sitter vacua in $\alpha'$-complete cosmology

The $\alpha'$-complete cosmology developed by Hohm and Zwiebach classifies the ${\rm O}(d,d;{\mathbb R})$ invariant theories involving metric, $b$-field and dilaton that only depend on time, to all orders in $\alpha'$. Some of these theories feature non-perturbative isotropic de Sitter vacua in the string frame, generated by the infinite number of higher-derivatives of ${\rm O}(d,d;{\mathbb R})$ multiplets. Extending the isotropic ansatz, we construct stable and unstable non-perturbative de Sitter solutions in the string and Einstein frames. The generalized equations of motion admit new solutions, including anisotropic $d+1$-dimensional metrics and non-vanishing $b$-field. In particular, we find dS$_{n+1}\times T^{d-n}$ geometries with constant dilaton, and also metrics with bounded scale factors in the spatial dimensions with non-trivial $b$-field. We discuss the stability and non-perturbative character of the solutions, as well as possible applications.