  This article is an addendum to [1]. We extend our computation of the on-shell
scattering amplitudes in an arbitrary inflaton background $\bar{\phi}_1$.
Although the effective Einstein frame cutoff for $\bar{\phi}_1>>M_P/\sqrt{\xi}$
turns out to be $\bar{\phi}_1$ or $\xi\bar{\phi}_1$ for the $U(1)$ model, this
is not the case for the realistic doublet Higgs model where the effective
Einstein frame cutoff turns out to be the standard $M_P/\sqrt{\xi}$ for both
the Palatini and metric formulations. Then, as it has been pointed out in [1]
the background $\bar{\phi}_1$ is the effective Jordan frame cutoff for both the
Palatini and metric formulations.
