Large Slow Roll Parameters in Single Field Inflation

TL;DR

This paper analyzes scenarios in single-field inflation where large slow roll parameters affect mode behavior, including decay or growth outside the horizon, with analytical and numerical methods applied to transient fast-roll phases.

Contribution

It provides a detailed analysis of large slow roll parameters in inflation, especially during transient fast-roll phases, revealing their impact on mode evolution outside the horizon.

Findings

Large psilonnd modes decay outside the horizon.

Large \u03b4auses modes to grow outside the horizon.

Multiple large slow roll parameters lead to complex mode behaviors.

Abstract

We initially consider two simple situations where inflationary slow roll parameters are large and modes no longer freeze out shortly after exiting the horizon, treating both cases analytically. We then consider applications to transient phases where the slow roll parameters can become large, especially in the context of the common `fast-roll' inflation frequently used as a mechanism to explain the anomalously low scalar power at low $l$ in the CMB. These transient cases we treat numerically. We find when $\epsilon$, the first slow roll parameter, and only $\epsilon$ is large, modes decay outside the horizon, and when $\delta$, the second slow roll parameter, is large, modes grow outside the horizon. When multiple slow roll parameters are large the behavior in general is more complicated, but we nevertheless show in the 'fast-roll' inflation case, modes grow outside the horizon.