Constant-roll inflation driven by a scalar field with nonminimal derivative coupling

Abstract

In this work, we study constant-roll inflation driven by a scalar field with nonminimal derivative coupling to gravity, via the Einstein tensor. This model contains a free parameter, [Formula: see text], which quantifies the nonminimal derivative coupling and a parameter [Formula: see text] which characterizes the constant-roll condition. In this scenario, using the Hamilton–Jacobi-like formalism, an ansatz for the Hubble parameter (as a function of the scalar field) and some restrictions on the model parameters, we found new exact solutions for the inflaton potential which include power-law, de Sitter, quadratic hilltop and natural inflation, among others. Additionally, a phase-space analysis was performed and it is shown that the exact solutions associated to natural inflation and a “cosh-type” potential, are attractors.