Cosmological constant in SUGRA models with Planck scale SUSY breaking
  and degenerate vacua
  The empirical mass of the Higgs boson suggests small to vanishing values of
the quartic Higgs self--coupling and the corresponding beta function at the
Planck scale, leading to degenerate vacua. This leads us to suggest that the
measured value of the cosmological constant can originate from supergravity
(SUGRA) models with degenerate vacua. This scenario is realised if there are at
least three exactly degenerate vacua. In the first vacuum, associated with the
physical one, local supersymmetry (SUSY) is broken near the Planck scale while
the breakdown of the SU(2)_W\times U(1)_Y symmetry takes place at the
electroweak (EW) scale. In the second vacuum local SUSY breaking is induced by
gaugino condensation at a scale which is just slightly lower than \Lambda_{QCD}
in the physical vacuum. Finally, in the third vacuum local SUSY and EW symmetry
are broken near the Planck scale.
