New non-perturbative de Sitter vacua in α′-complete cosmology

Abstract

The α′-complete cosmology developed by Hohm and Zwiebach classifies the O(d, d; ℝ) invariant theories involving metric, b-field and dilaton that only depend on time, to all orders in α′. Some of these theories feature non-perturbative isotropic de Sitter vacua in the string frame, generated by the infinite number of higher-derivatives of O(d, d; 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 dSn+1× Td−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.

Cosmology at the top of the α′ tower

“…Zwiebach [42,43] (generalizing [44]), who found the form of the most general action for the metric, the dilaton and the b-field when these fields only depend on time, which is invariant under O(d, d) transformations and which includes α corrections to all orders. The inclusion of coupling to other matter fields was then first explored in [45], and applications to string cosmology have been explored in a few studies so far [42,43,[45][46][47][48][49][50], often discovering new potential solutions, such as de Sitter-like or loitering backgrounds, which are otherwise often difficult to find in string cosmology (see, e.g., [51][52][53][54]). The current paper's aim is to go beyond these recent works on string-cosmology backgrounds to all orders in α .…”

“…Had the two-form field been non-vanishing, other corrections would have been present as multi-trace operators. The explicit derivation of the EOMs and search for solutions in this case has been recently obtained in [50] in the absence of matter, while another approach which includes matter and specific conditions so that these multi-trace corrections can be ignored has recently been developed in [56]. Nonetheless, some of the following results apply even with full O(d, d) symmetry, and these cases will be explicitly discussed.…”

“…Note that, in the latter case, one really means exact dS spacetime since the dilaton is constant, and hence, there is no distinction between the string frame and the Einstein frame. While the fact that adding matter with EoS p t = −ρ to the system yields a dS solution is not a surprise, 11 finding a dS solution in vacuum and in the Einstein frame 12 is quite unusual, though this was first discovered in [50].…”

Cosmological α′-corrections from the functional renormalization group

“…The resulting mini-superspace effective actions involve a single function of the Hubble parameter, whose perturbative expansion ought to match the α expansion order by order. Recent works have investigated some phenomenological aspects of effective actions of this type [33][34][35][36]. This remarkable result provides our starting point: combining the consistency constraints of string theory with FRG methods can potentially shed light on string theory at large curvature.…”

Kalb-Ramond backgrounds in α′-complete cosmology

“…There has already been one fundamental milestone towards this direction. In [16], the EOMs in vacuum were derived for anisotropic cosmological backgrounds in the presence of an arbitrary two-form field. In our paper, we consider a more restrictive ansatz which allows us to work with only the simplest set of α corrections that appear as single-trace contributions of arbitrary powers ofṠ 2 M N in the action.…”