Dynamical fine-tuning of initial conditions for small field inflations

TL;DR

This paper demonstrates that the initial conditions for small-field inflation can be dynamically realized through preheating effects, removing the need for fine-tuning and solving a key naturalness problem.

Contribution

It introduces a mechanism where preheating dynamically sets suitable initial conditions for small-field inflation without fine-tuning.

Findings

Initial conditions can be set dynamically after preheating.

The initial field value is much smaller than the potential scale.

This mechanism alleviates the initial condition problem in certain inflation models.

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 $\phi$ 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.