Natura Non Facit Saltum: An Analytical Model of Smooth Slow-Roll to Ultra-Slow-Roll Transition

TL;DR

This paper introduces an analytical single-field inflation model that smoothly transitions from slow-roll to ultra-slow-roll, providing explicit solutions and insights into the curvature power spectrum during the transition.

Contribution

It presents the first analytical model of a smooth slow-roll to ultra-slow-roll transition in inflation, with a simple modification to the effective mass term.

Findings

Analytical solutions for background and perturbations are derived.

The model's power spectrum dependence on parameters is explicitly characterized.

Comparison with sharp-transition models highlights distinctive signatures.

Abstract

In this letter, we propose a single-field inflation model that realizes a slow-roll-to-ultra-slow-roll transition while keeping the second slow-roll parameter smoothly varying throughout. The model is built through a minimal modification by introducing a simple time dependence in the effective mass term of the Mukhanov-Sasaki equation. We obtain fully analytical solutions for both the background evolution and the curvature perturbations, which makes the parameter dependence of the curvature power spectrum easy to track. To the best of our knowledge, this is the first analytical model that describes a smooth transition of this kind. We also compare its signatures with those of the corresponding sharp-transition counterpart.