Clockwork axions in cosmology. Is chromonatural inflation chrononatural?

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 for an axion of fundamental period F-a will obey the constraint < F-a. For a 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.