Models of Higgsed CP and their Cosmology

We discuss the phenomenological consequences of a gauged CP symmetry in the context of the Nelson–Barr solution to the strong CP problem. Exactly stable domain walls form when CP is spontaneously broken, and must be inflated away to recover a viable cosmology. We discuss the severe consequences for models of inflation and baryogenesis, and the tension with the “Nelson–Barr Quality Problem”, which sets an upper bound on the scale at which CP is broken. Finally, we present an explicit chiral model in which the bound on the CP-breaking scale is ameliorated.