Some inflationary models under the light of Planck 2018 results

In this work we study four well-known inflationary scenarios that are reported by the most recent Planck observations: Natural inflation, Hilltop quartic inflation, Starobinsky inflationary model, and Large field power-law potentials $V(\phi)\sim \phi^{p}$, considering $p=\sfrac{2}{3}, \sfrac{4}{3}$. The analysis is done using both the slow-roll approximation and the numerical solution to the background and perturbation equations. We show that the numerical solution improved the precision of these models with respect to the contour plot $r$ vs. $n_\sca$, having a lower $r$ in each model compared to the value calculated from the slow-roll approximation.