We introduce a time-dependent perturbation method to calculate the number of created particles in a 1D cavity with an oscillating wall of the frequency Ω. This method makes it easy to find the dominant part of the solution which results from the parametric resonance. The maximal number of particles are created at the mode frequency Ω/2. Using the Floquet theory, we discuss the long-time behavio...

We show that the most general inflaton potential in Minkowski spacetime for which the differential equation for the Fourier modes of the matter fields reduces to Lamé’s equation is of the form V (φ) = λφ/4 + Kφ/2 + μ/(2φ) + V0. As an application, we study the preheating phase after inflation for the above potential with K = 0 and arbitrary λ, μ > 0. For certain values of the coupling constant b...