(Quasi-) de Sitter solutions across dimensions and the TCC bound

Abstract

In this work, we investigate the existence of string theory solutions with a $d$-dimensional (quasi-) de Sitter spacetime, for $3\le d\le 10$. Considering classical compactifications, we derive no-go theorems valid for general $d$. We use them to exclude (quasi-) de Sitter solutions for $d\ge 7$. In addition, such solutions are found unlikely to exist in $d=6,5$. For each no-go theorem, we further compute the $d$-dependent parameter $c$ of the swampland de Sitter conjecture, $M_p\frac{|\nabla V|}{V}\ge c$. Remarkably, the TCC bound $c\ge \frac{2}{\sqrt{(d-1)(d-2)}}$ is then perfectly satisfied for $d\ge 4$, with several saturation cases. However, we observe a violation of this bound in $d=3$. We finally comment on related proposals in the literature, on the swampland distance conjecture and its decay rate, and on the so-called accelerated expansion bound.

49 pages; v3: minor modifications

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• Negative scalar potentials and the swampland: an Anti-Trans-Planckian Censorship Conjecture
• Quantum gravity constraints on scale separation and de Sitter in five dimensions
• Charged Nariai black holes on the dark bubble
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Supersymmetric Horizons at the Edge of Effective Field Theory
• Breaking Free from the Swampland of Impossible Universes through the DESI Portal
• Constraining Spatial Curvature with Priors from Swampland Conjectures