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 simultaneously. 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.
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