Dynamical fine-tuning of initial conditions for small field inflations

Abstract

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 $ϕ$ is coupled to another scalar field $χ$ through the interaction $g^2 χ^2 ϕ^2$ and the vacuum energy during the small field inflation is given by $λM^4$, the initial value can be dynamically set at $(\sqrtλ/g) M^2/M_{\rm pl}$, 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.