Phase transitions and vacuum tunneling into charge- and color-breaking minima in the MSSM

The scalar potential of the MSSM may have local and global minima characterized by nonzero expectation values of charged and colored bosons. Even if the true vacuum is not color and charge conserving, the early Universe is likely to occupy the minimum of the potential in which only the neutral Higgs fields have nonzero VEV's. The stability of this false vacuum with respect to quantum tunneling imposes important constraints on the values of the MSSM parameters. We analyze these constraints using some novel methods for calculating the false vacuum decay rate. Some regions of the MSSM parameter space are ruled out because the lifetime of the corresponding physically acceptable false vacuum is small in comparison to the present age of the Universe. However, there is a significant fraction of the parameter space that is consistent with the hypothesis that the Universe rests in the false vacuum that is stable on a cosmological time scale.