Conditions for (No) Eternal Inflation

Abstract

We construct analytic and numerical solutions of the Fokker-Planck equation that arises in the context of stochastic inflation. We use these solutions to derive necessary conditions for eternal inflation on the higher derivatives of the scalar field potential and examine the prospects for eternal inflation in a variety of popular models. We note similarities between the conditions needed to avoid eternal inflation and several recently-proposed Swampland criteria, which leads us to speculate on the possibility that the de Sitter Swampland conjectures should be viewed as approximate consequences of a No Eternal Inflation principle.