  A pseudo Nambu-Goldstone boson (pNGB) is a natural candidate of dark matter
in that it avoids the severe direct detection bounds. We show in this paper
that the pNGB has another different and interesting face with a higher symmetry
breaking scale. Such large symmetry breaking is motivated by various physics
beyond the standard model. In this case, the pNGB interaction is suppressed due
to the Nambu-Goldstone property and the freeze-out production does not work
even with sufficiently large portal coupling. We then study the pNGB dark
matter relic abundance from the out-of-equilibrium production via feeble Higgs
portal coupling. Further, a possibility is pursued the symmetry breaking scalar
in the pNGB model plays the role of inflaton. The inflaton and dark matter are
unified in a single field and the pNGB production from inflaton decay is
inevitable. For these non-thermally produced relic abundance of pNGB dark
matter and successful inflation, we find that the dark matter mass should be
less than a few GeV in the wide range of the reheating temperature and the
inflaton mass.
