Dynamics of Scalar Fields and Baryogenesis on their Backgrounds

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Electroweak baryogenesis is based on the idea that baryon asymmetry arises at the electroweak phase transition era. On the electroweak interaction, the standard model is established and there are many experimental data of accelerators. It is charming to interpret the baryon asymmetry of universe by the standard model(or its supersymmetric version) and many papers are written.It is dynamics of scalar fields(Higgs fields) to determine the electroweak phase transition. It is pointed out that the electroweak phase transition is preferred to be the first order in the minimal supersymmetric standard model(MSSM). Among 3 conditions of Sakharov, nonequilibrium is satisfied by the growth of bubble walls and baryon number violation is due to sphaleron transition. On large CP violation, we propose the transitional CP violation where tiny explicit CP violation enlarges through the spontaneous CP violation. This proposal reproduced the observations well and gave an impact to other groups. However, this model restricts the Higgs mass and experimental data have the tendency to exceed the restrictions.To overcome this difficulty, we need to consider the extension of MSSM, that is, Next-to-MSSM. Here, we introduce the scalar field of SU (2) singlet. The scalar field couples to Higgs fields and relax mass restrictions of Higgs fields. We can find the parameter spaces that are consistent with experiments.On the other hand, the finite temperature effective potential of NMSSM shows the multi-step phase transition other than the first and second transition. In MSSM, light-stop loop contributes the first order phase transition. In NMSSM, heavy-stop loop can contribute the first order phase transition.The contribution of SU (2) singlet scalar can deform the sphaleron solution of SU (2) gauge and Higgs system. We are now analyzing the solutions.Finally, we will calculate the generation probability of baryon asymmetry in the NMSSM.