Sound speed and viscosity of semi-relativistic relic neutrinos

Generalized fluid equations, using sound speed c_eff² and viscosity c_vis² as effective parameters, provide a convenient phenomenological formalism for testing the relic neutrino "null hypothesis," i.e. that that neutrinos are relativistic and free-streaming prior to recombination. In this work, we relax the relativistic assumption and ask "to what extent can the generalized fluid equations accommodate finite neutrino mass?" We consider both the mass of active neutrinos, which are largely still relativistic at recombination m² / T² ∼ 0.2, and the effect of a semi-relativistic sterile component. While there is no one-to-one mapping between mass/mixing parameters and c_eff² and c_vis², we demonstrate that the existence of a neutrino mass could induce a bias to measurements of c_eff² and c_vis² at the level of 0.01 m² / T² ∼ 10^-3.