ar X iv : h ep - p h / 06 11 37 8 v 1 2 9 N ov 2 00 6 Dark energy and the hierarchy problem

The well-known hierarchy between the Planck scale (∼ 10GeV) and the TeV scale, namely a ratio of ∼ 10 between the two, is coincidentally repeated in a inverted order between the TeV scale and the dark energy scale at ∼ 10eV implied by the observations. We argue that this is not a numerical coincidence. The same brane-world setups to address the first hierarchy problem may also in principle address this second hierarchy issue. Specifically, we consider supersymmetry in the bulk and its breaking on the brane and resort to the Casimir energy induced by the bulk graviton-gravitino mass-shift on the brane as the dark energy. For the ADD model we found that our notion is sensible only if the number of extra dimension n = 2. We extend our study to the Randall-Sundrum model. Invoking the chirality-flip on the boundaries for SUSY-breaking, the zero-mode gravitino contribution to the Casimir energy does give rise to the double hierarchy. Unfortunately since the higher Kaluza-Klein modes acquire relative mass-shifts at the TeV level, the zero-mode contribution to Casimir energy is overshadowed.