  CP violation of the SM is insufficient to explain the baryon asymmetry in the
universe and therefore an additional source of CP violation is needed. Here the
extension of the SM by a neutral complex scalar singlet with a nonzero vacuum
expectation value (cSMCS) plus a heavy vector quark pair is considered. This
model offers the spontaneous CP violation and proper description in the
baryogenesis, it leads strong enough first-order electro-weak phase transition
to suppress the baryon-violating sphaleron process.
