  In the electroweak phase transition there arises the problem of baryon number
washout by sphaleron transitions, which can be avoided if the phase transition
is strongly enough first order. The minimal supersymmetric standard model has
just two Higgs doublets H1 and H2, while the next to minimal model, NMSSM, has
an additional singlet, N, this latter giving rise to the helpful feature that
the Higgs potential contains a tree level trilinear field term. We use the
tunneling criterion for the existence of a first order electroweak phase
change. A quantitative statistical analysis indicates that with parameters of
the NMSSM satisfying the experimental constraints a strong first order phase
change occurs in about 50% of cases.
