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

TL;DR

This paper explores the existence of (quasi-) de Sitter solutions in string theory across various dimensions, deriving no-go theorems, analyzing the swampland conjecture parameter c, and examining the TCC bound's validity, especially noting violations in three dimensions.

Contribution

It provides dimension-dependent no-go theorems for (quasi-) de Sitter solutions and analyzes the swampland de Sitter conjecture parameter c in relation to the TCC bound across dimensions.

Findings

No (quasi-) de Sitter solutions for d ≥ 7.

TCC bound c ≥ 2/√((d-1)(d-2)) satisfied for d ≥ 4.

Violation of TCC bound observed in d=3.

Abstract

In this work, we investigate the existence of string theory solutions with a $d$-dimensional (quasi-) de Sitter spacetime, for $3 \leq d \leq 10$. Considering classical compactifications, we derive no-go theorems valid for general $d$. We use them to exclude (quasi-) de Sitter solutions for $d \geq 7$. 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, $M_p \frac{|\nabla V|}{V} \geq c$. Remarkably, the TCC bound $c \geq \frac{2}{\sqrt{(d-1)(d-2)}}$ is then perfectly satisfied for $d \geq 4$, 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.