  In 'hilltop inflation', inflation takes place when the inflaton field slowly
rolls from close to a maximum of its potential (i.e. the 'hilltop') towards its
minimum. When the inflaton potential is associated with a phase transition,
possible topological defects produced during this phase transition, such as
domain walls, are efficiently diluted during inflation. It is typically assumed
that they also do not reform after inflation, i.e. that the inflaton field
stays on its side of the 'hill', finally performing damped oscillations around
the minimum of the potential. In this paper we study the linear and the
non-linear phases of preheating after hilltop inflation. We find that the
fluctuations of the inflaton field during the tachyonic oscillation phase grow
strong enough to allow the inflaton field to form regions in position space
where it crosses 'over the top of the hill' towards the 'wrong vacuum'. We
investigate the formation and behaviour of these overshooting regions using
lattice simulations: Rather than durable domain walls, these regions form
oscillon-like structures (i.e. localized bubbles that oscillate between the two
vacua) which should be included in a careful study of preheating in hilltop
inflation.
