Dynamical fine-tuning of initial conditions for small field inflations
  Small-field inflation (SFI) is widely considered to be unnatural because an
extreme fine-tuning of the initial condition is necessary for sufficiently
large e-folding. In this paper, we show that the unnaturally-looking initial
condition can be dynamically realised without any fine-tuning if the SFI occurs
after rapid oscillations of the inflaton field and particle creations by
preheating. In fact, if the inflaton field $\phi$ is coupled to another scalar
field $\chi$ through the interaction $g^2 \chi^2 \phi^2$ and the vacuum energy
during the small field inflation is given by $\lambda M^4$, the initial value
can be dynamically set at $(\sqrt{\lambda}/g) M^2/M_{\rm pl}$, which is much
smaller than the typical scale of the potential $M.$ This solves the initial
condition problem in the new inflation model or some classes of the hilltop
inflation models.
