# Constant-roll inflation driven by a scalar field with non-minimal derivative coupling

## TL;DR

This paper explores constant-roll inflation driven by a scalar field with non-minimal derivative coupling, deriving new exact solutions and analyzing their stability, which enhances understanding of inflationary models with derivative couplings.

## Contribution

It introduces new exact solutions for inflation with non-minimal derivative coupling using the Hamilton-Jacobi formalism and analyzes their attractor behavior.

## Key findings

- Derived new exact inflaton potentials including power-law and natural inflation.
- Identified attractor solutions associated with natural inflation and a cosh-type potential.
- Provided phase space analysis confirming stability of certain inflationary solutions.

## Abstract

In this work, we study constant-roll inflation driven by a scalar field with non-minimal derivative coupling to gravity, via the Einstein tensor. This model contains a free parameter, $\eta$, which quantifies the non-minimal derivative coupling and a parameter $\alpha$ which characterize 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.