  With the assistance of a complex singlet, and an effective operator involving
CP violations, the dark matter relic abundance and baryon asymmetry of the
universe have been addressed simul- taneously. We studied the electroweak
baryogenesis mechanism systematically. The electroweak phase transition
analysis indicates that the strong first order phase transition takes place by
one- step or two-step type due to the dynamics of the energy gap between the
electroweak vacuum and the vacuum of the complex singlet. The relation between
the magnitude of baryon asymmetry of the universe and the phase transition type
and strength has been explored in the framework of electroweak baryogenesis.
