Numerical Study of Some Generalizations of the Starobinsky Inflationary Model

In this work, we perform a numerical study of three Starobinsky--type inflationary scenarios: the $\alpha$--Starobinsky inflationary model, the power--law Starobinsky inflationary model, and the power--law $\alpha$--Starobinsky inflationary model. For an appropriate choice of parameters, each scenario reproduces the standard Starobinsky limit. For each case, we derive the relevant slow--roll expressions in order to compute numerically the scalar and tensor power spectra over the corresponding parameter space and evaluate the associated inflationary observables. Finally, we provide a comparative analysis in the $(n_\sca,A_\sca)$ and $(r,n_\sca)$ parameter spaces using contour plots. Our results indicate that, for certain choices of parameters, the $\alpha$--Starobinsky model and the power--law $\alpha$--Starobinsky model are favored by \textit{Planck} 2018 observations.