Dark Energy from Casimir Energy on Noncommutative Extra Dimensions

TL;DR

This paper explores how Casimir energy on noncommutative extra dimensions with topology $S^2$ can account for dark energy, linking quantum geometry with cosmological observations.

Contribution

It introduces a model where noncommutative geometry of extra dimensions generates a positive energy density consistent with dark energy observations.

Findings

Energy density is positive and matches dark energy levels.

Extra dimension size aligns with experimental constraints.

Correct commutative limit is recovered as noncommutativity vanishes.

Abstract

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.