On the de Sitter swampland criterion

TL;DR

The paper addresses the tension between the proposed de Sitter swampland criterion, which forbids de Sitter extrema in 4d effective theories, and the existence of 10d classical de Sitter solutions in type II supergravity. It presents three avenues to reconcile these results: (i) questioning the trustworthiness of the 10d solutions due to backreaction and smearing of sources, (ii) arguing that the corresponding 4d low-energy theories on group manifolds are not true low-energy EFTs because of scale hierarchies, and (iii) introducing a refined criterion that couples the existence and stability of de Sitter solutions. The analysis suggests that 10d constructions may lie outside valid 4d EFT descriptions and that a more nuanced swampland criterion is warranted, potentially allowing tachyonic de Sitter states while excluding stable ones. These insights help clarify under which conditions string-theoretic compactifications can yield consistent low-energy cosmologies and guide future tests of swampland conjectures.

Abstract

A new swampland criterion has recently been proposed. As a consequence, it forbids the existence of de Sitter solutions in a low energy effective theory of a quantum gravity. However, there exist classical de Sitter solutions of ten-dimensional (10d) type II supergravities, even though they are unstable. This appears at first sight in contradiction with the criterion. Beyond possible doubts on the validity of these solutions, we propose two answers to this apparent puzzle. A first possibility is that the known 10d solutions always exhibit an energy scale of order or higher than a Kaluza-Klein scale, as we argue. A corresponding 4d low energy effective theory would then differ from the usual consistent truncations, and as we explain, would not admit a de Sitter solution. This would reconcile the existence of these 10d de Sitter solutions with the 4d criterion. A second, alternative possibility is to have a refined swampland criterion, that we propose. It forbids to have both the existence and the stability of a de Sitter solution, while unstable solutions are still allowed.