Refining the boundaries of the classical de Sitter landscape

David Andriot,Johan Blåbäck

doi:10.1007/jhep03(2017)102

Abstract

We derive highly constraining no-go theorems for classical de Sitter backgrounds of string theory, with parallel sources; this should impact the embedding of cosmological models. We study ten-dimensional vacua of type II supergravities with parallel and backreacted orientifold Op-planes and Dp-branes, on four-dimensional de Sitter spacetime times a compact manifold. Vacua for p = 3, 7 or 8 are completely excluded, and we obtain tight constraints for p = 4, 5, 6. This is achieved through the derivation of an enlightening expression for the four-dimensional Ricci scalar. Further interesting expressions and no-go theorems are obtained. The paper is self-contained so technical aspects, including conventions, might be of more general interest.

Highlights

We derive highly constraining no-go theorems for classical de Sitter backgrounds of string theory, with parallel sources; this should impact the embedding of cosmological models
Relevant to us are vacua where the spacetime is the warped product of a four-dimensional de Sitter space-time and a six-dimensional compact internal manifold M: with a controlled value of the dilaton, this would be a valid classical background of string theory
Standard ones for classical de Sitter vacua with compact internal geometries [18,19,20,21] are circumvented by requiring orientifolds

Summary

Compactification setting

We consider ten-dimensional type IIA and IIB supergravities and use the conventions given in appendix A. If for instance M is a fibered manifold and the transverse subspace is the base, one can find examples where this property holds Thanks to these properties, the Bianchi identities (BI) for F410 and F510 impose f4 and f5 to be closed; the RR BI can be restricted to the internal forms Fk only, towards dFk − H ∧ Fk−2 = −εp 2κ210 Tp cp δ9⊥−p. Where one should only consider even/odd RR fluxes in IIA/IIB, and we used the above properties (we only used Point 1 through 4 for the sources), giving in particular gMN TMN=μν = 4T10/(p + 1) These scalar equations will be combined to express R4 in terms of a limited number of ingredients. We will make use of the BI which will allow us to put further restrictions on the possibility of de Sitter vacua

First manipulations

Outlook

A Type II supergravities

B Dp-brane energy minimization and calibration

Findings

C Computational details