  In N=1 supergravity the tree-level scalar potential of the hidden sector may
have a minimum with broken local supersymmetry (SUSY) as well as a
supersymmetric Minkowski vacuum. These vacua can be degenerate, allowing for a
consistent implementation of the multiple point principle. The first minimum
where SUSY is broken can be identified with the physical phase in which we
live. In the second supersymmetric phase, in flat Minkowski space, SUSY may be
broken dynamically either in the observable or in the hidden sectors inducing a
tiny vacuum energy density. We argue that the exact degeneracy of these phases
may shed light on the smallness of the cosmological constant. Other possible
phenomenological implications are also discussed. In particular, we point out
that the presence of such degenerate vacua may lead to small values of the
quartic Higgs coupling and its beta function at the Planck scale in the
physical phase.
