Clockwork Axions in Cosmology: Is Chromonatural Inflation Chrononatural?

TL;DR

This paper examines whether clockwork mechanisms can explain large axion-gauge field couplings in cosmology, finding constraints that challenge certain UV completions like clockwork, and discussing alternative approaches and their implications.

Contribution

It analyzes the feasibility of clockwork constructions for axion models with large couplings, revealing constraints that limit their applicability in cosmological theories.

Findings

Clockwork constructions impose a bound  < F_a on the scale  in the potential.

Clockwork may not be viable for sub-Planckian field ranges in chromonatural inflation.

Alternative methods like large charge fields or kinetic mixing have limitations or require lighter axions.

Abstract

Many cosmological models rely on large couplings of axions to gauge fields. Examples include theories of magnetogenesis, inflation on a steep potential, chiral gravitational waves, and chromonatural inflation. Such theories require a mismatch between the axion field range and the mass scale appearing in the $a F \widetilde{F}$ coupling. This mismatch suggests an underlying monodromy, with the axion winding around its fundamental period a large number of times. We investigate the extent to which this integer can be explained as a product of smaller integers in a UV completion: in the parlance of our times, can the theory be "clockworked"? We argue that a clockwork construction producing a potential $\mu^4 \cos(\frac{a}{j F_a})$ for an axion of fundamental period $F_a$ will obey the constraint $\mu < F_a$. For some applications, including chromonatural inflation with sub-Planckian field range, this constraint obstructs a clockwork UV completion. Alternative routes to a large coupling include fields of large charge (an approach limited by strong coupling) or kinetic mixing (requiring a lighter axion). Our results suggest that completions of axion cosmologies that explain the large parameter in the theory potentially alter the phenomenological predictions of the model.