Tree-level unitarity in Higgs inflation in the metric and the Palatini
  formulation
  We calculate the tree-level amplitudes for electrically neutral $2\to2$
scattering for the Standard Model Higgs doublet non-minimally coupled to the
Ricci scalar. We consider both the metric and the Palatini formulation of
gravity. We find the partial wave unitarity limit for a general background
field value. Our results are in agreement with previous work. In the
electroweak vacuum, tree-level unitarity is violated at $\sim
M_\text{Planck}/\xi$ in the metric formulation, and at $\sim
M_\text{Planck}/\sqrt{\xi}$ in the Palatini formulation. In the inflationary
large field background, the unitarity limit is at $\sim
M_\text{Planck}/\sqrt{\xi}$ in both formulations. We compare the unitarity
violation energy to scales relevant during inflation. We also calculate a
direct collider limit on $\xi$ in the Palatini formulation,
$\xi<2.5\times10^{31}$.
