Dark Energy from Casimir Energy on Noncommutative Extra Dimensions

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.

6 pages, RevTeX4

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Cited by in corpus (4)

• Finite Temperature Casimir Effect in Kaluza-Klein Spacetime
• Finite temperature Casimir effect in spacetime with extra compactified dimensions
• Zero point energy on extra dimension: Noncommutative Torus
• Interacting Quintessence and Growth of Structure