  Building on the success of the Starobinsky model in describing the
inflationary period of the universe, we investigate two simple generalizations
of this model and their constraints imposed by the reheating epoch. The first
generalization takes the form $R^{2p}$, while the second is the
$\alpha$-Starobinsky model. We first focus on the case where $p=1$ or
equivalently, $\alpha=1$, which corresponds to the original Starobinsky model.
We derive exact consistency relations between observables and cosmological
quantities, without neglecting any terms, and impose the reheating condition $0
< \omega_{re} < 0.25$, where $\omega_{re}$ is the equation of state parameter
at the end of reheating. This allows us to obtain new bounds for $n_s$ and $r$
that satisfy this condition and apply them to other observables and
cosmological quantities. We repeat this process for the cases where $p \neq 1$
and $\alpha \neq 1$ and find that these generalizations only result in minor
modifications of the Starobinsky model, including the potential and the bounds
on observables and cosmological quantities.
