  Higher-order theories of gravity are extensions to general relativity (GR)
motivated mainly by high-energy physics searching for GR ultraviolet
completeness. They are characterized by the inclusion of correction terms in
the Einstein-Hilbert action that leads to higher-order field equations. In this
paper, we propose investigating inflation due to the GR extension built with
all correction terms up to the second-order involving only the scalar curvature
$R$, namely, $R^{2}$, $R^{3}$, $R\square R$. We investigate inflation within
the Friedmann cosmological background, where we study the phase space of the
model, as well as explore inflation in slow-roll leading-order. Furthermore, we
describe the evolution of scalar perturbations and properly establish the
curvature perturbation. Finally, we confront the proposed model with recent
observations from Planck, BICEP3/Keck, and BAO data.
