Nonminimal coupling inflation with constant slow roll

Abstract

In this paper, we study a single-field inflationary model modified by a nonminimal coupling term between the Ricci scalar [Formula: see text] and the scalar field [Formula: see text] in the context of constant-roll inflation. The first-order formalism is used to analyze the constant-roll inflation instead of the standard methods used in the literature. In principle, the formalism considers two functions of the scalar field, [Formula: see text] and [Formula: see text], which lead to the reduction of the equations of motion to first-order differential equations. The approach can be applied to a wide range of cosmological situations since it directly relates the function [Formula: see text] with Hubbles parameter [Formula: see text]. We perform the inflationary analysis for power-law and exponential couplings, separately. Then, we investigate the features of constant-roll potentials as inflationary potentials. Finally, we compare the inflationary parameters of the models with the observations of Cosmic Microwave Background (CMB) anisotropies in view of realizing a physically motivated model.