  We study the possibility that dark energy is a manifestation of the Casimir
energy on extra dimensions with the topology of $S^2$. We consider our universe
to be $M^4 \times S^2$ and modify the geometry by introducing noncommutativity
on the extra dimensions only, i.e. replacing $S^2$ with the fuzzy version
$S_{F}^2$. We find the energy density as a function of the size of the
representation $M+1$ of the algebra of $S_{F}^2$, 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.

High Energy Physics - Theory