Spontaneous CP violation at the electroweak scale

Utilizing results on the cosmology of anomalous discrete symmetries we show that models of spontaneous CP violation can in principle avoid the domain wall problem. A small but nonzero QCD explicitly breaks CP and can lift the degeneracy of the two CP conjugate vacua, so the domain walls become unstable, but can survive to cosmologically interesting epochs. We explore this in the context of a two-Higgs-doublet model. In this context, we show that axion solutions of the strong CP problem cannot be implemented without further extensions of the Higgs sector or other new physics.