Preheating with extra dimensions

We investigate preheating in a higher-dimensional generalized Kaluza-Klein theory with a quadratic inflaton potential $V(\phi)=\frac12 m^2\phi^2$ including metric perturbations explicitly. The system we consider is the multi-field model where there exists a dilaton field $\sigma$ which corresponds to the scale of compactifications and another scalar field $\chi$ coupled to inflaton with the interaction $\frac12 g^2\phi^2\chi^2+\tilde{g}^2\phi^3\chi$. In the case of $\tilde{g}=0$, we find that the perturbation of dilaton does not undergo parametric amplification while the $\chi$ field fluctuation can be enhanced in the usual manner by parametric resonance. In the presence of the $\tilde{g}^2\phi^3\chi$ coupling, the dilaton fluctuation in sub-Hubble scales is modestly amplified by the growth of metric perturbations for the large coupling $\tilde{g}$. In super-Hubble scales, the enhancement of the dilaton fluctuation as well as metric perturbations is weak, taking into account the backreaction effect of created $\chi$ particles. We argue that not only is it possible to predict the ordinary inflationary spectrum in large scales but extra dimensions can be held static during preheating in our scenario.