Refining the boundaries of the classical de Sitter landscape

TL;DR

This work addresses the existence of classical de Sitter vacua in ten-dimensional type II supergravity with parallel D_p/O_p sources. By working directly with the ten-dimensional equations of motion and Bianchi identities, the authors derive an explicit expression for the four-dimensional Ricci scalar $\tilde{{\cal R}}_4$ that separates negative flux and curvature contributions from positive, total-derivative terms. They prove no-go results for $p=3,7,8$ and obtain strong curvature-based constraints for $p=4,5,6$, effectively narrowing the classical de Sitter landscape in this setup. The findings have practical implications for uplifting cosmological models within string theory and guide future explorations toward intersecting-brane configurations or calibrated-source analyses. All results are presented in a self-contained framework with detailed conventions and methods.

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 space-time 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.