Comparison of cosmological models to current data shows that the presence of a non-trivial feature in the primordial power spectrum of fluctuations, around the scale 120/h Mpc, is an open and exciting
possibility, testable in a near future. This could set new constraints on inflationary models. We will focus on a supersymmetric model with two U(1) gauge symmetries, associated with two Fayet-Iliopoulos terms. This model involves a fast second-order phase transition during inflation, with a stage of spinodal instability, and an interruption of slow-roll. We simulate numerically the evolution of quantum fluctuations, taking into account the spinodal modes, and we show that the semi-classical approximation can be employed at any time, due to the presence of a second inflaton field. The primordial power spectrum possesses a rich structure, including a non-Gaussian spike on observable scales.