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Spontaneous CP Violation and Baryogenesis in the Minimal Supersymmetric Standard Model

We investigate the effects of the spontaneous CP violation at finite temperature in the Minimal Supersymmetric Standard Model on the baryogenesis at the weak scale. After a brief discussion of the case in which the electroweak phase transition is of the second order, we study in details the baryogenesis scenario when the transition proceeds via bubble nucleation. We show that the space-time dependent phase for the Higgs vacuum expectation values coming from the spontaneous CP violation can give rise to a efficient generation of baryon number inside the bubble walls if the superpotential parameters and the soft supersymmetry breaking ones are complex. However we find that in order to get the observed value for the baryon asymmetry of the universe the phases of such parameters can be as small as $10^{-5}$, giving rise to an electron dipole moment of the neutron well below the current experimental limit. Moreover a light Higgs pseudoscalar is needed, and an upper bound on its mass is obtained.