Nonminimal coupling inflation with constant slow roll

Abstract

We study a single field inflationary model modified by a non-minimal coupling term between the Ricci scalar $R$ and the scalar field $\phi$ in the context of constant-roll inflation. The first-order formalism is used to analyse the constant-roll inflation instead of the standard methods used in the literature. In principle, the formalism considers two functions of the scalar field, $W=W(\phi )$ and $Z=Z(\phi )$, 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 Hubble 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 CMB anisotropies in view of realize a physically motivated model.

15 pages, 6 figures, Accepted for publication in Int. J. Mod. Phys. D

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