Ultraviolet Unitarity Violations in Higgs'-Coupled Starobinsky Inflation Model

We perform the calculation for tree-level ultraviolet unitarity violation scales for Higgs' inflation models involving $R^2$ term as performed in \cite{Antoniadis2021} by adding an interaction between said $R^2$ term and the Higgs' field, 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. Naively, the violations are seen to come only from graviton-mediated processes and terms that can be traced back to the $R^2$ correction. However, taking into account recent works \cite{McDonald_2021, Antoniadis2021, antoniadis2022addendum} that debunk these naive predictions, we find that the scattering amplitudes considered in this work are well-behaved, suggesting that this model would remain free from tree-level unitarity violations up to the Planck scale