  We propose a novel possibility for Higgs inflation where the perturbative
unitarity below the Planck scale is ensured by construction and the successful
predictions for inflation are accommodated. The conformal gravity coupling for
the Higgs field leads to the proximity of the effective Planck mass to zero in
the Jordan frame during inflation, corresponding to a pole in the Higgs kinetic
term in the Einstein frame. Requiring the Higgs potential to vanish at the
conformal pole in the effective theory in the Jordan frame, we make a robust
prediction of the successful Higgs inflation. For a successful Higgs inflation
at the pole, we take the running quartic coupling for the Higgs field to be
small enough at the inflation scale, being consistent with the low-energy data,
but we need a nontrivial extension of the SM with extra scalar or gauge fields
in order to keep the running Higgs quartic coupling small during inflation.
Performing the perturbative analysis of reheating with the known couplings of
the SM particles to the Higgs boson, we show that a concrete realization of the
Higgs pole inflation can be pinned down by the reheating processes with a
general equation of state for the Higgs inflaton. We illustrate some extensions
of the simple Higgs pole inflation to the general pole expansions, the running
Higgs quartic coupling in the Standard Model and its extension with a singlet
scalar field, a supergravity embedding of the Higgs pole inflation.
