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

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 .