Eternal Hilltop Inflation

TL;DR

This paper analyzes eternal inflation in hilltop models, showing that despite finite support for eternal inflation regions, the overall volume continues to be dominated by inflating regions at any finite time, regardless of energy scale.

Contribution

It demonstrates that hilltop inflation models support eternal inflation with finite support regions, and the volume dominance persists at any energy scale, contrasting with other models.

Findings

Eternal inflation occurs in hilltop models with finite support regions.

The expansion rate during eternal inflation matches the slow roll rate.

The volume of inflating regions dominates at any finite time, regardless of energy scale.

Abstract

We consider eternal inflation in hilltop-type inflation models, favored by current data, in which the scalar field in inflation rolls off of a local maximum of the potential. Unlike chaotic or plateau-type inflation models, in hilltop inflation the region of field space which supports eternal inflation is finite, and the expansion rate $H_{EI}$ during eternal inflation is almost exactly the same as the expansion rate $H_*$ during slow roll inflation. Therefore, in any given Hubble volume, there is a finite and calculable expectation value for the lifetime of the "eternal" inflation phase, during which quantum flucutations dominate over classical field evolution. We show that despite this, inflation in hilltop models is nonetheless eternal in the sense that the volume of the spacetime at any finite time is exponentially dominated by regions which continue to inflate. This is true regardless of the energy scale of inflation, and eternal inflation is supported for inflation at arbitrarily low energy scale.