Numerical Study of Some Generalizations of the Starobinsky Inflationary Model

TL;DR

This paper numerically investigates generalized Starobinsky inflation models, analyzing their predictions for inflationary observables and comparing them with Planck 2018 data.

Contribution

It introduces and compares three generalized Starobinsky inflation models, deriving slow-roll expressions and analyzing their compatibility with observational data.

Findings

Certain parameter choices favor models consistent with Planck 2018 observations.

All models reproduce the standard Starobinsky limit under specific parameters.

Contour plots illustrate the parameter spaces compatible with observational constraints.

Abstract

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.