Clockwork Axions in Cosmology: Is Chromonatural Inflation Chrononatural?

TL;DR

The paper investigates whether clockwork/alignment can UV-complete the large axion–gauge couplings used in cosmological models like chromonatural and Anber–Sorbo inflation. It derives a unitarity-based bound $\mu \lesssim F_a$ that constrains clockwork realizations and shows how this bound propagates through two-site and N-site clockwork constructions. Through explicit analysis of Anber–Sorbo inflation and chromonatural inflation, the authors demonstrate that clockwork alone cannot account for the required coupling in sub-Planckian setups, necessitating either very large charges or alternative mechanisms such as kinetic mixing, which come with their own phenomenological implications. The results imply that UV completions feasible for axion cosmologies may substantially affect the predicted observational signatures, highlighting the need for careful UV model-building when interpreting large-parameter axion cosmologies.

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 $μ^4 \cos(\frac{a}{j F_a})$ for an axion of fundamental period $F_a$ will obey the constraint $μ< F_a$. 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.

Figures (1)

• Figure 1: Viable parameter space for chromonatural inflation. We assume the number of e-folds of inflation, $N_e = 60$, and $\Delta_{\mathcal{R}}^2=2.2\times10^{-9}$ as well as other theoretically motivated constraints discussed in the text. The red regions show the allowed parameter space for particular values of $k$. The white region is the union of all such regions. The fact that large $k$ is required indicates that clockwork alone cannot explain the large coupling in chromonatural inflation.