Nonlinearity analysis for cosmological inflation with minimal and non-minimal coupling of scalar field from horndeski theory for special cases: de sitter expansion and decaying scalar field

Abstract

In this work, we consider De Sitter expansion and decaying scalar field in cosmological model with combination of minimal and non-minimal coupling of scalar field from Horndeski theory. As a continuity of the previous work, after the background solution and condition obtained, we continue the analysis to the nonlinearity aspect of perturbations via the spectral index of the perturbations. Spectral index of the perturbations and tensor to-scalar ratio of these special cases give sign of inflation model.