The dark side of the Littlest Seesaw: freeze-in, the two right-handed neutrino portal and leptogenesis-friendly fimpzillas

We propose a minimal model to simultaneously account for a realistic neutrino spectrum through a type-I seesaw mechanism and a viable dark matter relic density. The model is an extension of the Littlest Seesaw model in which the two right-handed neutrinos of the model are coupled to a Z(2)-odd dark sector via right-handed neutrino portal couplings. In this model, a highly constrained and direct link between dark matter and neutrino physics is achieved by considering the freeze-in production mechanism of dark matter. We show that the neutrino Yukawa couplings which describe neutrino mass and mixing may also play a dominant role in the dark matter production. We investigate the allowed regions in the parameter space of the model that provide the correct neutrino masses and mixing and simultaneously give the correct dark matter relic abundance. In certain cases the right-handed neutrino mass may be arbitrarily large, for example in the range 10(10) - 10(11) GeV required for vanilla leptogenesis, with a successful relic density arising from frozen-in dark matter particles with masses around this scale, which we refer to as "filmpzillas".