Baryogenesis constraints on two Higgs doublet models

The requirement that sphaleron transitions be sufficiently suppressed after the electroweak phase transition to preserve any then existing baryon asymmetry is studied perturbatively in a general two Higgs doublet model. We find that about 5% of otherwise acceptable Higgs potentials evade baryon number washout and that the presence of a soft CP violating term makes it easier to do so. The spectrum of Higgs particles for these acceptable cases is discussed. The Minimal Supersymmetric Standard Model is treated as a special case; here we only find acceptable cases in an otherwise disfavoured region of parameter space, tan β<1.