Dark energy from Casimir energy on noncommutative extra dimensions

We study the possibility that dark energy is a manifestation of the Casimir energy on extra dimensions with the topology of S². We consider our universe to be M⁴×S² and modify the geometry by introducing noncommutativity on the extra dimensions only, i.e. replacing S² with the fuzzy version S_F². We find the energy density as a function of the size of the representation M+1 of the algebra of S_F², and we calculate its value for the M+1=2 case. The value of the energy density turns out to be positive, i.e. provides dark energy, and the size of the extra dimensions agrees with the experimental limit. We also recover the correct commutative limit as the noncommutative parameter goes to zero.

©2006 The American Physical Society