Superfluidity in neutrino clusters

We study the formation of a superfluid condensate of neutrinos inside a neutrino cluster. The attractive interaction between neutrinos is mediated by a scalar boson which is lighter than a neutrino. We consider the appearance of neutrino bound states consisting of particles with oppositely directed spins. The gap equation for such a system is derived. Based on numerical simulations of the neutrino distribution in a cluster, we find the phase transition temperature and the coherence length inside such a cluster for various parameters of the system. The constraints on the parameters of the Yukawa interaction, resulting in the neutrino superfluidity, are derived. We obtain that the cosmic neutrino background can contribute to the superfluid condensate inside a neutrino cluster having realistic characteristics. The mechanism of the neutrino cluster cooling in the early universe, based on the plasmons \v{C}erenkov radiation, is proposed.