Dynamical Analysis of Attractor Behavior in Constant Roll Inflation

Abstract

There has been considerable recent interest in a new class of non-slow roll inflationary solutions known as \textit{constant roll} inflation. Constant roll solutions are a generalization of the ultra-slow roll (USR) solution, where the first Hubble slow roll parameter $\epsilon$ is small, but the second Hubble slow roll parameter $\eta$ is not. While it is known that the USR solutions represent dynamical transients, there has been some disagreement in literature about whether or not large-$\eta$ constant roll solutions are attractors or are also a class of transient solutions. In this paper we show that the large-$\eta$ constant roll solutions do in fact represent transient solutions by performing stability analysis on the exact analytic (large-$\eta$) constant roll solutions.