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 $(n_{\text{sca}},A_{\text{sca}})$ and $(r,n_{\text{sca}})$ 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 $\mathit{\text{Planck}}$ 2018 observations.