The Inflationary Dynamics with the Scalar-Tensor Model

We investigate the cosmic inflation within a class of the scalar-tensor model with the scalar-dependent non-minimal kinetic couplings. The inflationary dynamical potential will be applied. Using the slow-roll approximation, we compute theoretical predictions for the key observables, like the spectral indexes $n_s$, scalar-to-tensor ratio $r$ and the running of the scalar spectral index $\alpha_s$ in terms of the free parameters of the model. Besides, we find the limitations of these parameters. In addition, these quantities will be compared with the latest observational data from the Planck data. Furthermore, we analyze the sensitivity of $r$, $n_s$ and $\alpha_s$ in terms of the model's free parameters.