Intermediate inflation in generalized non-minimal derivative coupling model

Abstract

In this work, we consider intermediate inflation in context of the Generalized Non-Minimal Derivative Coupling (GNMDC) model. In this model, inflation is driven by a canonical scalar field that is coupled not only to gravity but also to the derivative of the scalar field. The GNMDC model introduces new dynamics and features during the inflationary epoch. We find inflationary solutions with a power law scalar field for the power law coupling function. Additionally, we determine the inflaton potential that generates intermediate expansion of the scale factor. We also discuss the background equations in the high friction limit and derive constraints on the parameters of our model. Furthermore, we investigate the cosmological perturbations in the slow roll approximation within the GNMDC model, We calculate the scalar and tensor spectral index and the tensor-to-scalar ratio during the intermediate inflation. We compare the results of this model with the observational data that can be used to test the model using the cosmic microwave background radiation data. Overall, we establish conditions for the inflaton potential that ensure the continuation of accelerated expansion during the slow roll inflation. We numerically analyze the power spectrum and spectral index for scalar and tensor modes in intermediate inflation in the high friction limit. Moreover, we use the Planck 2018 data, to obtain constraints on the parameters of the model. We demonstrate that intermediate inflation in the GNMDC model is successful in evaluation and explanation of the background and perturbational quantities using observational data.