THE ELECTROWEAK PHASE-TRANSITION IN MINIMAL SUPERGRAVITY MODELS

We explore the electroweak phase transition in minimal supergravity mo dels by extending our previous analysis of the one-loop Higgs potentia l to include finite temperature effects. Minimal supergravity is chara cterized by two Higgs doublets at the electroweak scale, gauge couplin g unification, and universal soft-SUSY breaking at the unification sca le. We have searched for the allowed parameter space where the phase t ransition is sufficiently first order to avoid washout of baryon numbe r after the phase transition via unsuppressed anomalous electroweak sp haleron processes. This requirement imposes strong constraints on the Higgs sector; we find m(h) less than or similar to 60 GeV (at one loop ) and tan beta less than or similar to 2. We argue that present Higgs searches rule out this remaining parameter space. Thus, if supergravit y (with two light Higgs doublets) is to allow for baryogenesis, it mus t also provide for B-L production at or above the weak scale. Our resu lts therefore indicate that the field/coupling content of minimal supe rgravity is insufficient to account for the baryon asymmetry of the un iverse (BAU). We suggest that the no-scale flipped SU(5) supergravity model naturally and economically provides a source of B-L violation an d can account for the observed ratio n(B)/n(7) similar to 10(-10).