New non-perturbative de Sitter vacua in ${\alpha }^{\prime }$-complete cosmology

Abstract

The ${\alpha }^{\prime }$-complete cosmology developed by Hohm and Zwiebach classifies the $\mathrm{O}(d,d;\mathbb{R})$ invariant theories involving metric, $b$-field and dilaton that only depend on time, to all orders in ${\alpha }^{\prime }$. Some of these theories feature non-perturbative isotropic de Sitter vacua in the string frame, generated by the infinite number of higher-derivatives of $\mathrm{O}(d,d;\mathbb{R})$ 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.

arXiv comment52 pages, 2 figures; v2: 53 pages, 2 figures, discussions, references and acknowledgements added

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