  We consider the possibility that the inflaton is part of the dark sector and
interacts with the standard model through a portal interaction with a heavy
complex scalar field in equilibrium with the standard model at high energies.
The inflaton and dark matter are encapsulated in a single complex field and
both scalar sectors are charged under different (approximate) global U(1)'s
such that the dark matter, as well as the visible pseudo-scalar are taken to be
relatively light, as pseudo Nambu-Goldstone bosons of the theory. The dark
matter relic density is populated by Freeze-In productions through the inflaton
portal. In particular, after the reheating, production of dark matter by
inflaton decay is naturally suppressed thanks to Planck stringent constraints
on the dark quartic coupling, therefore preserving the non thermal scenario
from any initial condition tuning.
