Dynamical fine-tuning of initial conditions for small field inflations

International audienceSmall-field inflation (SFI) is widely considered to be unnatural because anextreme fine-tuning of the initial condition is necessary for sufficientlylarge e-folding. In this paper, we show that the unnaturally-looking initialcondition can be dynamically realised without any fine-tuning if the SFI occursafter rapid oscillations of the inflaton field and particle creations bypreheating. In fact, if the inflaton field $\phi$ is coupled to another scalarfield $\chi$ through the interaction $g^2 \chi^2 \phi^2$ and the vacuum energyduring the small field inflation is given by $\lambda M^4$, the initial valuecan be dynamically set at $(\sqrt{\lambda}/g) M^2/M_{\rm pl}$, which is muchsmaller than the typical scale of the potential $M.$ This solves the initialcondition problem in the new inflation model or some classes of the hilltopinflation models