Tunneling in Axion Monodromy

TL;DR

This paper reevaluates the tunneling rate in axion monodromy models, finding that the Coleman formula often does not apply, but it remains valid in some regimes relevant to inflation, with implications for the relaxion scenario.

Contribution

It derives a new tunneling rate estimate for axion monodromy models that accounts for the limitations of Coleman's assumptions, improving accuracy in certain parameter regimes.

Findings

Coleman formula often inaccurate for axion monodromy

New estimate aligns with Coleman in large field inflation regimes

Implications for relaxion scenario discussed

Abstract

The Coleman formula for vacuum decay and bubble nucleation has been used to estimate the tunneling rate in models of axion monodromy in recent literature. However, several of Coleman's original assumptions do not hold for such models. Here we derive a new estimate with this in mind using a similar Euclidean procedure. We find that there are significant regions of parameter space for which the tunneling rate in axion monodromy is not well approximated by the Coleman formula. However, there is also a regime relevant to large field inflation in which both estimates parametrically agree. We also briefly comment on the applications of our results to the relaxion scenario.