  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.
