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 $p=\text{sfrac}23,\text{sfrac}43$. 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. $n_{\text{sca}}$, having a lower $r$ in each model compared to the value calculated from the slow-roll approximation.