Cosmological domain wall evolution and spontaneous CP violation from a gauge singlet scalar sector

We consider the evolution of domains of different spontaneous CP violating phase which form during a cosmological phase transition in a simple model of gauge singlet scalars. This model can in principle be coupled to the Standard Model in order to provide the additional CP violation necessary during the electroweak phase transition in order to allow for a successful electroweak baryogenesis scenario, provided that the domains resulting in negative baryon number, which would be produced in the limit of purely spontaneous CP violation in equal numbers along with the domains resulting in positive baryon number, are eliminated prior to the electroweak phase transition. We show that it is possible to eliminate the negative baryon number domains by the introduction of an explicit CP violating phase in the singlet scalar potential, which can be as small as O(10−15) in the case where the singlet scalars have a mass scale ≲ 1 TeV. The possibility that such a small explicit phase could have a gravitational origin is briefly discussed.