  Recently, the problem of unitarity violation during the preheating stage of
Higgs inflation with a large non-minimal coupling has been much discussed in
the literature. We point out that this problem can be translated into a strong
coupling problem for the dimensionless effective coupling, and that the
existence of these problems is highly dependent on the choice of
higher-dimensional operators because they can significantly change the
background dynamics and the canonical normalization of the fluctuations around
it. Correspondingly, the typical energy of particles produced during the first
stage of preheating can remain comparable to or below the cutoff scale of the
theory. As an example, we numerically calculate the particle production in the
presence of a specific four-derivative operator of the Higgs field, and confirm
the statement above. Our argument also applies to multi-field inflation with
non-minimal couplings.
