Dark Energy density in models with Split Supersymmetry and degenerate   vacua
  In N=1 supergravity supersymmetric (SUSY) and non-supersymmetric Minkowski vacua originating in the hidden sector can be degenerate. In the supersymmetric phase in flat Minkowski space non-perturbative supersymmetry breakdown may take place in the observable sector, inducing a non-zero and positive vacuum energy density. Assuming that such a supersymmetric phase and the phase in which we live are degenerate, we estimate the value of the cosmological constant. We argue that the observed value of the dark energy density can be reproduced in the Split-SUSY scenario of the supersymmetry breaking if the SUSY breaking scale is of order of 10^{10} GeV. 
C. Froggatt, R. Nevzorov, H. B. Nielsen
hep-ph astro-ph.CO gr-qc hep-th