We perform the calculation for tree-level ultraviolet unitarity violation
scales for Higgs’-$R^2$ inflation models by including an additional
$R^2\phi^2$-type term, as suggested in \cite{Mathew:2017lvh}. Due to certain
constraints, we resort to the Einstein frame for our calculations, where we
separate our analysis between metric and Palatini formulations. We follow
recent works \cite{Hertzberg:2010dc,McDonald_2021, Antoniadis2021,
antoniadis2022addendum} that debunk the naive predictions based on dimension
counting to accurately estimate the behaviour of scattering amplitudes we find.
This also helps us put constraints on coupling parameters involved in the
theory for which the unitarity would remain intact even as we approach the
Planck scale, without having to incorporate new degrees of freedom.
