  Higgs G-inflation is an inflation model that takes advantage of a
Galileon-like derivative coupling. It is a non-renormalizable operator and is
strongly coupled at high energy scales. Perturbative analysis does not have a
predictive power any longer there. In general, when the Lagrangian is expanded
around the vacuum, the strong coupling scale is identified as the mass scale
that appears in non-renormalizable operators. In inflationary models, however,
the identification of the strong coupling scale is subtle, since the structures
of the kinetic term as well as the interaction itself can be modified by the
background inflationary dynamics. Therefore, the strong coupling scale depends
on the background. In this letter, we evaluate the strong coupling scale of the
fluctuations around the background in the Higgs G-inflation including the
Nambu-Goldstone modes associated with the symmetry breaking. We find that the
system is sufficiently weakly coupled when the scales which we now observe exit
the horizon during inflation and the observational predictions with the
semiclassical treatment are valid. However, we also find that the inflaton
field value at which the strong coupling scale and the Hubble scale meet is
less than the Planck scale. Therefore, we cannot describe the model from the
Planck scale, or the chaotic initial condition.
