Interplay between neutrino and gravity portals for FIMP dark matter

In the classic type I seesaw mechanism with very heavy right-handed (RH) neutrinos, it is possible to account for dark matter via RH neutrino portal couplings to a feebly interacting massive particle (FIMP) dark sector. However, for large RH neutrino masses, gravity can play an important role. We study the interplay between the neutrino portal through the right-handed neutrinos and the gravity portal through the massless spin-2 graviton in producing dark matter particles in the early universe. As a concrete example, we consider the minimal and realistic Littlest Seesaw model with two RH neutrinos, augmented with a dark scalar and a dark fermion charged under a global $U(1)_D$ dark symmetry. In the model, the usual seesaw neutrino Yukawa couplings and the right-handed neutrino masses (the lightest being about $5times 10^{10}$ GeV) are fixed by neutrino oscillations data and leptogenesis. Hence, we explore the parameter space of the two RH neutrino portal couplings, the two dark particle masses and the reheating temperature of the universe, where the correct dark matter relic abundance is achieved through the freeze-in mechanism. In particular, we highlight which class of processes dominate the dark matter production. We find that, despite the presence of the gravity portal, the dark matter production relies on the usual seesaw neutrino Yukawa coupling in some regions of the parameter space, so realising a direct link between dark matter and neutrino phenomenology. Finally, we report the threshold values for the neutrino portal couplings below which the neutrino portal is irrelevant and the Planckian Interacting Dark Matter paradigm is preserved.