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

A bstract 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 M p ∣ ∇ V ∣ V ≥ c . Remarkably, the TCC bound c≥ 2√(d-1)(d-2) 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.