Note on initial conditions for small-field inflation

TL;DR

This paper demonstrates that quantum mechanically determined initial conditions, via a flattened potential region, can effectively guide small-field inflation towards slow-roll, reducing sensitivity to initial velocities and addressing the overshoot problem.

Contribution

It introduces a method to set initial conditions through a flattened potential region, enhancing the robustness of small-field inflation models.

Findings

Inflation is driven towards the slow-roll attractor exponentially fast.

The approach partially evades the overshoot problem.

An explicit example with a hilltop potential and ultra slow-roll plateau is provided.

Abstract

We show that initial conditions for small-field inflation can be determined quantum mechanically by introducing a suitable flattened region in the scalar potential. The inflaton is then driven towards the slow-roll attractor solution exponentially fast, desensitising inflation from the initial velocity and partially evading the so-called overshoot problem. We give an explicit example in the context of hilltop inflation by introducing an ultra slow-roll plateau around the maximum of the potential and analyse its effect on the phase-space trajectories.