  We present the conformal freeze-in (COFI) scenario for dark matter
production. At high energies, the dark sector is described by a gauge theory
flowing towards a Banks-Zaks fixed point, coupled to the standard model via a
non-renormalizable portal interaction. At the time when the dark sector is
populated in the early universe, it is described by a strongly coupled
conformal field theory. As the universe cools, cosmological phase transitions
in the standard model sector, either electroweak or QCD, induce conformal
symmetry breaking and confinement in the dark sector. One of the resulting dark
bound states is stable on the cosmological time scales and plays the role of
dark matter. With the Higgs portal, the COFI scenario provides a viable dark
matter candidate with mass in a phenomenologically interesting 0.1-1 MeV range.
With the quark portal, a dark matter candidate with mass around 1 keV is
consistent with observations. Conformal bootstrap puts a non-trivial constraint
on model building in this case.
