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 onestep 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.1 Which should be the strong first-order EWPT to protect the generated baryon asymmetry from washout and suppress the sphaleron after the process is ended.

We study the electroweak phase transition in the alignment limit of the CP-conserving two-Higgs-doublet model (2HDM) of Type I and Type II. The effective potential is evaluated at one-loop, where the thermal potential includes Daisy corrections and is reliably approximated by means of a sum of Bessel functions. Both 1-stage and 2-stage electroweak phase transitions are shown to be possible, depending on the pattern of the vacuum development as the Universe cools down. For the 1-stage case focused on in this paper, we analyze the properties of phase transition and discover that the field value of the electroweak symmetry breaking vacuum at the critical temperature at which the first order phase transition occurs is largely correlated with the vacuum depth of the 1-loop potential at zero temperature.We demonstrate that a strong first order electroweak phase transition (SFOEWPT) in the 2HDM is achievable and establish benchmark scenarios leading to different testable signatures at colliders. In addition, we verify that an enhanced triple Higgs coupling (including loop corrections) is a typical feature of the SFOPT driven by the additional doublet. As a result, SFOEWPT might be able to be probed at the LHC and future lepton colliders through Higgs pair production.