# Dynamical Analysis of Attractor Behavior in Constant Roll Inflation

## TL;DR

This paper investigates the stability of large-$ta$ constant roll inflation solutions, demonstrating through analysis that these solutions are transient rather than attractors, clarifying their dynamical role in inflation models.

## Contribution

The paper provides a stability analysis showing large-$ta$ constant roll solutions are transient, resolving previous disagreements in the literature.

## Key findings

- Large-$ta$ solutions are transient, not attractors.
- Stability analysis confirms the transient nature of these solutions.
- Clarifies the dynamical behavior of constant roll inflation models.

## 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.