A Possible Connection between Dark Energy and the Hierarchy∗

Recently it was suggested that the dark energy maybe related to the well-known hierarchy between the Planck scale (∼ 10GeV) and the TeV scale. The same brane-world setup to address this hierarchy problem may also in principle address the smallness problem of dark energy. Specifically, the Planck-SM hierarchy ratio was viewed as a quantum gravity-related, dimensionless fine structure constant where various physical energy scales in the system are associated with the Planck mass through different powers of the ‘gravity fine structure constant’. In this paper we provide a toy model based on the Randall-Sundrum geometry where SUSY-breaking is induced by the coupling between a SUSY-breaking Higgs field on the brane and the KK gravitinos. We show that the associated Casimir energy density indeed conforms with the dark energy scale.