Bounds on Slow Roll and the de Sitter Swampland

TL;DR

The paper addresses whether stable de Sitter vacua and slow-roll inflation can arise in a UV-complete theory of quantum gravity, proposing a refinement of the de Sitter swampland criterion that constrains slow-roll itself rather than solely ε_V. By recasting the bound in terms of the slow-roll parameter η_V and using scaling arguments in the volume-dilaton subspace of Type II compactifications, the authors derive explicit, order-one negative bounds on η_V for several tree-level tachyonic constructions (e.g., η_V ≤ -3.68 in 4D IIA and η_V ≤ -7.94 in 7D), showing that tachyonic instabilities align with the refined bound. They survey explicit Type II compactifications, finding tachyons with η_V in the range −2 to −4, which remains compatible with the proposed bound and helps explain difficulties in achieving long inflation. The discussion also considers potential evasion mechanisms, such as N-flation with many fields, and situates the refined bound within the broader debate on dark energy and inflation in string theory, highlighting its role as a constraint on tree-level constructions rather than a definitive no-go for the full theory.

Abstract

The recently introduced swampland criterion for de Sitter (arXiv:1806.08362) can be viewed as a (hierarchically large) bound on the smallness of the slow roll parameter $ε_V$. This leads us to consider the other slow roll parameter $η_V$ more closely, and we are lead to conjecture that the bound is not necessarily on $ε_V$, but on slow roll itself. A natural refinement of the de Sitter swampland conjecture is therefore that slow roll is violated at ${\cal O}(1)$ in Planck units in any UV complete theory. A corollary is that $ε_V$ need not necessarily be ${\cal O}(1)$, if $η_V \lesssim -{\cal O}(1)$ holds. We consider various tachyonic tree level constructions of de Sitter in IIA/IIB string theory (as well as closely related models of inflation), which superficially violate arXiv:1806.08362, and show that they are consistent with this refined version of the bound. The phrasing in terms of slow roll makes it plausible why both versions of the conjecture run into trouble when the number of e-folds during inflation is high. We speculate that one way to evade the bound could be to have a large number of fields, like in $N$-flation.

Figures (1)

• Figure 1: Plot of allowed values of $x\equiv V_{O_4}/V_{eff}$ and $y \equiv V_{R_6}/V_{eff}$, the region extends indefinitely to the right.