  Existence and properties of the electroweak phase transition in the early
universe depend strongly on the mass of the Higgs scalar M_H. There is
presumably no true symmetry restoration at high temperature. Nevertheless, a
first order phase transition occurs in the standard model for M_H smaller than
about 70 GeV. For a realistic scalar mass M_H larger than about 70 GeV the
transition to the high temperature regime is described by a crossover, due to
the strong electroweak gauge interactions for temperatures near and above the
critical temperature. Electroweak baryogenesis during this transition seems not
possible within the standard model. The observed baryon asymmetry in the
universe therefore implies the necessity of an extension of the standard model.
