Stabilization of Compactification Volume In a Noncommutative Mini-Super-Phase-Space

TL;DR

This paper demonstrates that noncommutativity in the momenta conjugate to internal space scale factors can stabilize the compactification volume in higher-dimensional Einstein gravity, transforming its behavior from power-law to oscillatory.

Contribution

It introduces a novel mechanism where noncommutativity among internal momenta stabilizes the internal space volume in higher-dimensional gravity models.

Findings

Noncommutativity induces oscillatory behavior in internal scale factors.

Stabilization of compactification volume is achieved through momentum noncommutativity.

Power-law behavior is controlled and transformed by noncommutative effects.

Abstract

We consider a class of generalized FRW type metrics in the context of higher dimensional Einstein gravity in which the extra dimensions are allowed to have different scale factors. It is shown that noncommutativity between the momenta conjugate to the internal space scale factors controls the power-law behavior of the scale factors in the extra dimensions, taming it to an oscillatory behavior. Hence noncommutativity among the internal momenta of the mini-super-\emph{phase}-space can be used to explain stabilization of the compactification volume of the internal space in a higher dimensional gravity theory.