Weakly first order cosmological phase transitions and fermion production

We study weakly first order cosmological phase transitions in finite temper ature field theories. Focusing on the standard electroweak theory and its m inimal supersymmetric extension, we identify the regimes of Higgs masses fo r which the phase transition in these models proceeds by significant phase mixing and the coarsening of the subsequent domain network. This dynamics i s distinct from that for strongly first order transitions, which proceed by the nucleation and propagation of critical bubbles. We describe how electr oweak baryogenesis might take place in these models, explaining how our new picture can relax the sphaleron washout bound of traditional scenarios. (C ) 2001 Elsevier Science B.V. All rights reserved.