Strong interactions preserve CP symmetry to extraordinary precision, despite lacking an obvious reason to do so. The most elegant solution to this `strong CP puzzle' introduces a new particle---the QCD axion---that dynamically relaxes CP violation to experimentally acceptable levels. As an added virtue, the axion can also account for the dark matter in the Universe.
In standard constructions, the axion is intrinsically periodic (`compact'). This introduces model-building overhead and well-known cosmological tensions: stringent isocurvature constraints, cosmic strings, and the domain wall problem.
I will discuss an alternative paradigm in which the axion is fundamentally non-compact, leading to a qualitatively different cosmological picture. During inflation, field fluctuations populate many would-be QCD vacua across our observable Universe. When the QCD potential turns on, each causal region relaxes independently, washing out CMB-scale isocurvature modes and forming domain walls without accompanying strings. A small tilt in the axion potential, built into this construction, is essential for consistency: it destabilizes the walls before the onset of Big Bang Nucleosynthesis and leaves a residual CP violation that cannot be relaxed away.
The framework provides a viable axion dark matter candidate and makes correlated, testable experimental predictions: gravitational waves from wall collapse, potentially observable with future pulsar timing arrays; and irreducible CP violation accessible to next-generation proton electric dipole moment searches. Observation of both signals would be a smoking gun.
I will close by briefly discussing a concrete realization in which this picture emerges naturally---Weyl-invariant Einstein-Cartan gravity. There, the axion and the potential tilt are built in, and the smallness of the latter is dictated by gravitational couplings. This same theory offers a unified perspective on the strong CP, hierarchy, and cosmological constant issues.
Videoconference via https://us02web.zoom.us/j/82249348474