(Quasi-) de Sitter solutions across dimensions and the TCC bound
Résumé
In this work, we investigate the existence of string theory solutions with a d-dimensional (quasi-) de Sitter spacetime, for 3≤d≤10. Considering classical compactifications, we derive no-go theorems valid for general d. We use them to exclude (quasi-) de Sitter solutions for d≥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, Mp|∇V|V≥c. Remarkably, the TCC bound c≥2√(d−1)(d−2) is then perfectly satisfied for d≥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.