Relic neutrinos: Physically consistent treatment of effective number of neutrinos and neutrino mass

We perform a model independent study of the neutrino momentum distribution at freeze-out, treating the freeze-out temperature as a free parameter. Our results imply that measurement of neutrino reheating, as characterized by the measurement of the effective number of neutrinos $N_\nu$, amounts to the determination of the neutrino kinetic freeze-out temperature within the context of the standard model of particle physics where the number of neutrino flavors is fixed and no other massless (fractional) particles arise. At temperatures on the order of the neutrino mass, we show how cosmic background neutrino properties i.e. energy density, pressure, particle density, are modified in a physically consistent way as a function of neutrino mass and $N_\nu$.