Excitation of Kaluza-Klein gravitational mode

TL;DR

This paper studies whether oscillations of extra-dimensional space can cause significant excitation of Kaluza-Klein modes via parametric resonance, finding that in narrow resonance regimes, such excitation is not catastrophic.

Contribution

It demonstrates that in the narrow resonance regime, oscillations of the compactification radius do not lead to dangerous excitation of Kaluza-Klein modes.

Findings

Kaluza-Klein mode excitation is suppressed in narrow resonance regimes.

Oscillating compactification radius causes mass oscillations of Kaluza-Klein modes.

No catastrophic quantum excitation of Kaluza-Klein modes occurs in the studied regime.

Abstract

We investigate excitation of Kaluza-Klein modes due to the parametric resonance caused by oscillation of radius of compactification. We consider a gravitational perturbation around a D-dimensional spacetime, which we compactify on a (D-4)-sphere to obtain a 4-dimensional theory. The perturbation includes the so-called Kaluza-Klein modes, which are massive in 4-dimension, as well as zero modes, which is massless in 4-dimension. These modes appear as scalar, vector and second-rank symmetric tensor fields in the 4-dimensional theory. Since Kaluza-Klein modes are troublesome in cosmology, quanta of these Kaluza-Klein modes should not be excited abundantly. However, if radius of compactification oscillates, then masses of Kaluza-Klein modes also oscillate and, thus, parametric resonance of Kaluza-Klein modes may occur to excite their quanta. In this paper we consider part of Kaluza-Klein modes which correspond to massive scalar fields in 4-dimension and investigate whether quanta of these modes are excited or not in the so called narrow resonance regime of the parametric resonance. We conclude that at least in the narrow resonance regime quanta of these modes are not excited so catastrophically.