Effect of inflation on parametric resonance during preheating

The effect of inflation on parametric resonance during preheating is investigated. The behaviour of the preheating scalar field during inflation is investigated and is found to become squeezed in cases ranging from small-scale cases to large-scale cases. However, the positive-frequency solution is usually adopted in the initial condition of the scalar field at preheating. Although large squeezing occurs during inflation, the difference in the comoving occupation number of particles nk between two initial conditions is shown to be not so large. Rather, the ratio nk varies from 0.2 to 5.0, depending on k. In order to clarify this situation, we introduce the squeeze formulation. The squeeze parameters r and φ are calculated not only in preheating, but also in inflation. Since the squeeze parameters are calculated from inflation to preheating, we can clarify the behaviour of the parametric resonance. In preheating, the behaviour of r is shown to remain relatively unchanged with respect to k; however, the squeeze angle φ displays different behaviour for large-scale cases and small-scale cases