Slow-roll solutions to inflationary potentials have been widely believed to be the only universal attractor. Over the past few years there has been growing interest in a new class of inflationary models known as constant-roll inflation. Constant-roll solutions are a generalization of “ultraslow roll” dynamics, where the first slow-roll parameter is small, but the second slow-roll parameter $\eta$ is larger than unity. In ultraslow roll inflation, the large-$\eta$ solution is a dynamical transient, relaxing exponentially to the attractor de Sitter solution. In the constant-roll generalization, recent papers have concluded that constant-roll inflation represents a new class of nonslow roll attractor solutions. In this paper we show that these attractor solutions are actually the usual slow-roll attractor, disguised by a parameter duality, and that the large-$\eta$ solutions, as in the case of ultraslow roll, represent a dynamical transient.

• Received 26 April 2018

DOI:https://doi.org/10.1103/PhysRevD.97.123519