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

Some inflationary models under the light of Planck 2018 results