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

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.