This work reviews the cosmological inflation model involving inverted minimal and non-minimal interactions between the scalar field ϕ and its derivatives with the space curvature tensor. The de Sitter exponential expansion and the decaying scalar field conditions are also reviewed to move the model towards the inflationary condition, where as a generator of inflation, the scalar field must decay at the end of time. The scalar and tensor perturbation equations, their respective spectral indices, and the tensor-to-scalar ratio have been calculated to study the nonlinearity of the reviewed model. It is shown that the spectral indices and tensor-to-scalar ratio of the model are in good agreement with the observational data.
                        
                        
                        
                        
                            
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