A non-compact QCD axion

We investigate the cosmology of an axion that is fundamentally non-compact. During inflation, fluctuations of the effectively massless field populate many QCD vacua, thereby evading conventional isocurvature constraints while generating domain walls -- without accompanying cosmic strings. A small non-QCD contribution to the axion potential is required to trigger the timely collapse of domain walls; as a consequence, a residual amount of CP violation in the strong sector must exist, potentially within reach of planned experiments. Non-compact axions can account for the entirety of the dark matter abundance, and the collapse of domain walls sources a stochastic gravitational-wave background at nanohertz frequencies. Such axion dynamics can be embedded in top-down constructions -- such as Weyl-invariant Einstein-Cartan gravity -- where the tilting of the axion potential arises automatically.