  We make use of the frame and gauge independent formalism for scalar and
tensor cosmological perturbations developed in Ref. [1] to show that the
physical cutoff for 2-to-2 tree level scatterings in Higgs inflation is above
the Planck scale M_P throughout inflation. More precisely, we found that in the
Jordan frame, the physical cutoff scale is $({\Lambda}/a)_J \gtrsim
\sqrt{M_P^2+{\xi}{\phi}^2}$, while in the Einstein frame it is $({\Lambda}/a)_J
\gtrsim M_P$, where $\xi$ is the nonminimal coupling and $\phi$ denotes the
Higgs vev during inflation. The dimensionless ratio of the physical cutoff to
the relevant Planck scale is equal to one in both frames, thus demonstrating
the physical equivalence of the two frames. Our analysis implies that Higgs
inflation is unitary up to the Planck scale, and hence there is no naturalness
problem in Higgs inflation. In this paper we only consider the graviton and
scalar interactions.
