Higher-order extension of Starobinsky inflation: initial conditions,
  slow-roll regime, and reheating phase
  The most current observational data corroborate the Starobinsky model as one
of the strongest candidates in the description of an inflationary regime.
Motivated by such success, extensions of the Starobinsky model have been
increasingly recurrent in the literature. The theoretical justification for
this is well grounded: higher-order gravities arise in high-energy physics in
the search for the ultraviolet completeness of general relativity. In this
paper, we propose to investigate the inflation due to the extension of the
Starobinsky model characterized by the inclusion of the $R^{3}$ term. We make a
complete analysis of the potential and phase space of the model, where we
observe the existence of three regions with distinct dynamics for the scalar
field. We can establish restrictive limits for the number of $e$-folds through
a study of the reheating and by considering the usual couplings of the standard
matter fields and gravity. Thereby, we duly confront our model with the
observational data from Planck, BICEP3/Keck, and BAO. Finally, we discuss how
the inclusion of the cubic term restricts the initial conditions necessary for
the occurrence of a physical inflation.
