Nonminimal coupling inflation with constant slow roll

In this paper, we study a single-field inflationary model modified by a nonminimal coupling term between the Ricci scalar R and the scalar field ϕ 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, W = W(ϕ) and Z = Z(ϕ), 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 W with Hubbles parameter H. 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.