Slow nucleation rates in Chain Inflation with QCD Axions or Monodromy

TL;DR

This paper demonstrates that chain inflation models using QCD axions or monodromy face fundamental issues due to slow tunneling rates, and explores potential modifications and alternatives to overcome these limitations.

Contribution

It provides a detailed calculation of bubble nucleation rates showing the failure of previous chain inflation proposals with QCD axions and monodromy, and discusses possible solutions and alternatives.

Findings

Tunneling rates are too slow for chain inflation with QCD axions.

Series of minima in monodromy models are too far apart for rapid tunneling.

Modifying gravity or using different axion-like potentials can potentially resolve the problem.

Abstract

The previous proposal (by two of us) of chain inflation with the QCD axion is shown to fail. The proposal involved a series of fast tunneling events, yet here it is shown that tunneling is too slow. We calculate the bubble nucleation rates for phase transitions in the thick wall limit, approximating the barrier by a triangle. A similar problem arises in realization of chain inflation in the string landscape that uses series of minima along the monodromy staircase around the conifold point. The basic problem is that the minima of the potential are too far apart to allow rapid enough tunneling in these two models. We entertain the possibility of overcoming this problem by modifying the gravity sector to a Brans-Dicke theory. However, one would need extremely small values for the Brans-Dicke parameter. Many successful alternatives exist, including other "axions" (with mass scales not set by QCD) or potentials with comparable heights and widths that do not suffer from the problem of slow tunneling and provide successful candidates for chain inflation.