Parametric amplification of density perturbations in the oscillating inflation model - art. no. 103505

We study the adiabatic density perturbation in the oscillating inflation mo del, proposed by Damour and Mukhanov. The recent study of cosmological pert urbations during reheating shows that the adiabatic fluctuation behaves lik e a perfect fluid and no significant amplification occurs on superhorizon s cales. In the oscillating inflation model, however, the accelerated expansi on takes place during the oscillating stage and there might be a possibilit y that the parametric amplification on small scales affects the adiabatic l ong-wavelength perturbation. We analytically show that the density perturba tion neglecting the metric perturbation can be amplified by the parametric resonance and the instability band becomes very broad during oscillating in flation. We examine this issue by solving the evolution equation for pertur bation numerically. We find that the parametric resonance is strongly suppr essed for the long-wave modes comparable to the Hubble horizon. The result indicates that the metric perturbation plays a crucial role in the evolutio n of scalar field perturbation. Therefore, in the single held case, there w ould be no significant imprint of oscillating inflation on the primordial s pectrum of the adiabatic perturbation. However, it could be expected that t he oscillating inflation model in the multifield system gives an enormous a mplification on large scales, which may lead to the production of primordia l black holes. [S0556-2821(99)04010-2].