Construction of inflationary scenarios with the Gauss-Bonnet term and nonminimal coupling

TL;DR

This paper explores inflationary models involving a scalar field nonminimally coupled to both the Ricci scalar and the Gauss-Bonnet term, generalizing previous models to produce a variety of scenarios with identical spectral index and perturbation amplitude but different tensor-to-scalar ratios.

Contribution

It introduces a method to extend inflationary models with the Gauss-Bonnet term to include nonminimal coupling with the Ricci scalar, creating diverse models with similar spectral properties.

Findings

Constructed models with the same $n_s$ and $A_s$ but varying $r$

Demonstrated the feasibility of nonminimal coupling in inflationary scenarios

Provided a framework for analyzing scalar perturbations in these models

Abstract

Inflationary models with a scalar field nonminimally coupled both with the Ricci scalar and with the Gauss-Bonnet term are studied. We propose the way of generalization of inflationary scenarios with the Gauss-Bonnet term and a scalar field minimally coupled with the Ricci scalar to the corresponding scenarios with a scalar field nonminimally coupled with the Ricci scalar. Using the effective potential, we construct a set of models with the same values of the scalar spectral index $n_s$ and the amplitude of the scalar perturbations $A_s$ and different values of the tensor-to-scalar ratio $r$.