[Paper Review] On stable compactification with Casimir-like potential

Uwe Guenther, S. Kriskiv+1 more|ArXiv.org|Jan 8, 1998

Quantum Electrodynamics and Casimir Effect5 references3 citations

TL;DR

This paper proposes a mechanism for stable compactification of extra dimensions in multidimensional cosmological models using a Casimir-like potential arising from quantum fluctuations of massless scalar fields. By formulating a Casimir-like ansatz for the energy density in higher-dimensional manifolds, the authors derive an effective potential in the Einstein conformal frame that stabilizes internal scale factors, achieving stable compactification for one and two internal spaces.

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.

Motivation & Objective

• To investigate stable compactification of extra dimensions in higher-dimensional cosmological models.
• To address the challenge of stabilizing internal scale factors in Kaluza-Klein-type compactifications.
• To explore the role of quantum vacuum fluctuations in generating a stabilizing potential.
• To extend the Casimir effect to multidimensional manifolds with multiple internal spaces.
• To derive an effective potential in the Einstein conformal frame that ensures stability against scale factor excitations.

Proposed method

• Formulates a Casimir-like ansatz for the energy density of massless scalar field fluctuations in higher-dimensional spacetime.
• Derives the effective potential for internal scale factors in the Einstein conformal frame via dimensional reduction.
• Applies the ansatz to models with one and two internal spaces to analyze stability conditions.
• Uses conformal transformation techniques to map the higher-dimensional action into a four-dimensional effective theory.
• Analyzes the potential's minima to determine stable compactification configurations.
• Considers quantum field fluctuations in curved compact manifolds to model zero-point energy contributions.

Experimental results

Research questions

• RQ1 Can a Casimir-like potential stabilize extra dimensions in multidimensional cosmological models?
• RQ2 How does the energy density of quantum fluctuations contribute to an effective potential for internal scale factors?
• RQ3 What conditions ensure stability against excitations of the internal scale factors in models with multiple compact dimensions?
• RQ4 How does the choice of Casimir-like ansatz affect the form of the effective potential in higher-dimensional gravity?
• RQ5 Can stable compactification be achieved in models with more than one internal space using this mechanism?

Key findings

• A stable compactification of extra dimensions is achieved through a Casimir-like potential generated by quantum fluctuations of massless scalar fields.
• The effective potential derived in the Einstein conformal frame exhibits minima that correspond to stable internal space configurations.
• For one internal space, the model yields a stable minimum in the potential, ensuring compactification stability.
• In the case of two internal spaces, the Casimir-like ansatz leads to a stable configuration with respect to scale factor excitations.
• The results are consistent with the journal publication in Gravitation and Cosmology, confirming the validity of the approach.
• The method successfully generalizes the Casimir effect to multidimensional cosmological models with multiple compact dimensions.