The QCD axion has important connections to early universe cosmology. For example, it is often said that isocurvature limits rule out a combination of high axion decay constant, fa, and high inflationary Hubble scale, HI. High scales are theoretically motivated, so it is important to ask how robust this constraint is. We demonstrate that this constraint is naturally evaded when the quartic coupling of the complex U(1)PQ-breaking field is small (e.g. ≲ 10-6). In this case, fa changes from a larger value during inflation to a smaller value in the later universe, suppressing isocurvature perturbations. Importantly, we show that in large parts of parameter space this solution is not jeopardised by overproduction of the axion through parametric resonance. The isocurvature bounds are thus dependent on UV physics. We have found that, even for the minimal QCD axion, large parts of UV parameter space at both high fa and high HI are in fact allowed, not ruled out by isocurvature constraints.
Graham et al. (Sat,) studied this question.