Phase transitions in the early universe (is there a strongly first order electroweak phase transition?)

After some introductory remarks about the prospects of first order phase transitions in the early universe, we discuss in some detail the electroweak phase transition. In the standard model case a clear picture is arising including perturbative and nonperturbative effects. Since in this case the phase transition is not strongly first order as needed for baryogenesis, we discuss supersymmetric variants of the standard model, the MSSM with a light stop(R) and a NMSSM model where this can be achieved. We conclude with some remarks about the technical procedure and about possible effects of a strongly first order electroweak phase transition including baryogenesis.