The well-known hierarchy between the Planck scale ( \sim 10 ^ { 19 } GeV ) and the TeV scale , namely a ratio of \sim 10 ^ { 16 } between the two , is coincidentally repeated in a inverted order between the TeV scale and the dark energy scale at \sim 10 ^ { -3 } eV 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 .