Addendum to "Ultraviolet behaviour of Higgs inflation models"

Abstract

This article is an addendum to [1]. We extend our computation of the on-shell scattering amplitudes in an arbitrary inflaton background ${\bar{\varphi }}_1$. Although the effective Einstein frame cutoff for ${\bar{\varphi }}_1>>M_P/\sqrt{\xi }$ turns out to be ${\bar{\varphi }}_1$ or $\xi {\bar{\varphi }}_1$ 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 ${\bar{\varphi }}_1$ is the effective Jordan frame cutoff for both the Palatini and metric formulations.

Comments: 8 pages, 0 figures added preprint number