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Tunneling in Axion Monodromy

Jon Brown, William Cottrell, Gary Shiu, Pablo Soler

TL;DR

This work revisits membrane-mediated tunneling in axion monodromy, deriving a Euclidean bounce action that accounts for the non-metastable, rolling-axion dynamics and the presence of a 3-form coupling. The authors show that Coleman’s vacuum-decay formula does not universally apply; in the inflation-relevant regime the tunneling action matches Coleman up to a factor of about 8, while other parameter regions yield substantial deviations. By mapping the key parameters to inflationary and relaxion scenarios and invoking the Weak Gravity Conjecture as a benchmark, they derive qualitative and semi-quantitative bounds on tunneling that can constrain large-field inflation and related models. Gravity is discussed but left for future, with the flat-space results expected to persist in the regime $V/M_p^4 \ll 1$, suggesting tunneling may not generically threaten axion-monodromy inflations.

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.

Tunneling in Axion Monodromy

TL;DR

This work revisits membrane-mediated tunneling in axion monodromy, deriving a Euclidean bounce action that accounts for the non-metastable, rolling-axion dynamics and the presence of a 3-form coupling. The authors show that Coleman’s vacuum-decay formula does not universally apply; in the inflation-relevant regime the tunneling action matches Coleman up to a factor of about 8, while other parameter regions yield substantial deviations. By mapping the key parameters to inflationary and relaxion scenarios and invoking the Weak Gravity Conjecture as a benchmark, they derive qualitative and semi-quantitative bounds on tunneling that can constrain large-field inflation and related models. Gravity is discussed but left for future, with the flat-space results expected to persist in the regime , suggesting tunneling may not generically threaten axion-monodromy inflations.

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.

Paper Structure

This paper contains 14 sections, 56 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Review of Axion Monodromy
  3. Tunneling Rate
  4. Meta-stable vacuum decay
  5. Bounces in axion monodromy
  6. $SO(4)$ and $SO(3)$ symmetric universes and bubbles
  7. Spherical Symmetry
  8. Cylindrical Symmetry
  9. Limiting Cases
  10. Small Bubbles: $\beta \ll \alpha$
  11. Large Bubbles: $\beta \gg \alpha$
  12. Interpretations for the Inflaton and the Relaxion
  13. Including Gravity
  14. Conclusions

Figures (4)

  • Figure 1: Two interpretations of the effective potential.
  • Figure 2: Potential for vacuum decay as studied by Coleman.
  • Figure 3: The profile of $\phi_s$ with $\mu\bar{r} = 10$.
  • Figure 4: Comparison of the action $B$ between the case studied by Coleman (orange) and the axion monodromy studied here (blue) before extremization with respect to $\bar{s}$.