We study the adiabatic density perturbation in the oscillating inflation model, proposed by Damour and Mukhanov. The recent study of cosmological perturbations during reheating shows that the adiabatic fluctuation behaves like a perfect fluid and no significant amplification occurs on superhorizon scales. In the oscillating inflation model, however, the accelerated expansion takes place during the oscillating stage and there might be a possibility that the parametric amplification on small scales affects the adiabatic long-wavelength perturbation. We analytically show that the density perturbation neglecting the metric perturbation can be amplified by the parametric resonance and the instability band becomes very broad during oscillating inflation. We examine this issue by solving the evolution equation for perturbation numerically. We find that the parametric resonance is strongly suppressed for the long-wave modes comparable to the Hubble horizon. The result indicates that the metric perturbation plays a crucial role in the evolution of scalar field perturbation. Therefore, in the single field case, there would be no significant imprint of oscillating inflation on the primordial spectrum of the adiabatic perturbation. However, it could be expected that the oscillating inflation model in the multifield system gives an enormous amplification on large scales, which may lead to the production of primordial black holes.

• Received 11 December 1998

DOI:https://doi.org/10.1103/PhysRevD.59.103505