On stable compactification with Casimir-like potential

TL;DR

This paper explores how Casimir-like effects can lead to stable compactification of extra dimensions in multidimensional cosmological models, providing new insights into internal space stabilization.

Contribution

It introduces a Casimir-like ansatz for energy density in models with multiple internal spaces, demonstrating stable configurations for one and two internal dimensions.

Findings

Stable compactification achieved via Casimir effect.

Stable configurations found for one and two internal spaces.

Effective potential derived in Einstein conformal frame.

Abstract

Multidimensional cosmological models with a higher dimensional space-time manifold are investigated under dimensional reduction. In the Einstein conformal frame, the effective potential for the internal scale factors is obtained. The stable compactification of the internal spaces is achieved due to the Casimir effect. In the case of more than one internal space a Casimir-like ansatz for the energy density of the massless scalar field fluctuations is proposed. Stable configurations with respect to the internal scale factor excitations are found in the cases of one and two internal spaces.