Excitation of Kaluza-Klein modes of U(1) field by parametric resonance

TL;DR

This paper investigates the excitation of Kaluza-Klein modes via parametric resonance in compactified extra dimensions, proposing a cosmological criterion to exclude certain models based on resonance conditions, and finds that a sphere compactification is not ruled out.

Contribution

It introduces a cosmological criterion based on parametric resonance to evaluate the viability of compactification models, specifically analyzing Kaluza-Klein modes of U(1) fields.

Findings

The criterion rules out models with specific resonance conditions.

Sphere compactification with a U(1) field is not excluded due to mild resonance.

The study connects resonance phenomena with constraints on extra-dimensional theories.

Abstract

In this paper, based on the theory of parametric resonance, we propose a cosmological criterion on ways of compactification: we rule out such a model of compactification that there exists a Kaluza-Klein mode satisfying $2m_{KK}=\omega_b$, where $m_{KK}$ is mass of the Kaluza-Klein mode and $\omega_b$ is the frequency of oscillation of the radius of the compact manifold on which extra dimensions are compactified. This is a restatement of the criterion proposed previously [S. Mukohyama, Phys. Rev. {\bf D57}, 6191 (1998)]. As an example, we consider a model of compactification by a sphere and investigate Kaluza-Klein modes of U(1) field. In this case the parametric resonance is so mild that the sphere model is not ruled out.