On inflationary models in f(R,T) gravity with a kinetic coupling term

Abstract

We investigate inflationary models in [Formula: see text] modified gravity with a kinetic coupling term [Formula: see text] having a positive factor needed to remove the ghosts. Taking [Formula: see text], we calculate and analyze the relevant observable quantities including the spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text] using the slow-roll approximations. Concretely, we consider two scenarios described by the decoupling and the coupling behaviors between the scalar potential and the [Formula: see text] gravity via the moduli space by dealing with two potentials being the quartic one [Formula: see text] and the small field inflation [Formula: see text]. For the quartic inflation model, we consider a decoupling behavior. For the small field inflation, however, we present the parameter decoupling and coupling scenarios. For both scenarios, we compute and inspect [Formula: see text] and [Formula: see text] showing interesting results. For three different values of the number of e-folds [Formula: see text] and 70, we find that the coupling between [Formula: see text] and the scalar potential via the moduli space provides an excellent agreement with the observational findings. In the last part of this work, we provide a possible discussion on the amplitude of the scalar power spectrum needed to provide a viability of the proposed theory. Considering the second potential form in the parameter coupling scenario, we find acceptable values in certain points of the moduli space.