Bounds on Slow Roll and the de Sitter Swampland

TL;DR

This paper refines the de Sitter swampland conjecture by proposing that slow roll itself, rather than just the parameter epsilon_V, is bounded in UV complete theories, supported by string theory models and inflation scenarios.

Contribution

It introduces a refined conjecture that slow roll is violated at order one in Planck units, providing a new perspective on the de Sitter swampland criteria and analyzing string theory constructions.

Findings

String theory models are consistent with the refined bound.

High e-fold number inflation faces challenges with the conjecture.

Large field models like N-flation may evade the bound.

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 $\epsilon_V$. This leads us to consider the other slow roll parameter $\eta_V$ more closely, and we are lead to conjecture that the bound is not necessarily on $\epsilon_V$, 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 $\epsilon_V$ need not necessarily be ${\cal O}(1)$, if $\eta_V \lesssim -{\cal O}(1)$ 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.