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.
