Parametric resonance after hilltop inflation caused by an inhomogeneous inflaton field

We study preheating after hilltop inflation where the inflaton couples to another scalar field, e.g. a right-handed sneutrino, which provides a mechanism for generating the correct initial conditions for inflation and also a decay channel for the inflaton that allows for reheating and non-thermal leptogenesis. In the presence of such a coupling, we find that after the phases of tachyonic preheating and tachyonic oscillations, during which the inflaton field becomes inhomogeneous, there can be a subsequent preheating phase where the fluctuations of the other field get resonantly enhanced, from initial vacuum fluctuations up to amplitudes of the same order (and even larger) as the ones of the inflaton field. This resonant enhancement differs from the usual parametric resonance as the inflaton field is inhomogeneous at the time the enhancement takes place. We study this effect using lattice simulations as well as semi-analytically with a generalized Floquet analysis for inhomogeneous background fields.