Dynamical friction in the primordial neutrino sea

Standard big bang cosmology predicts a cosmic neutrino background at $T_\nu \simeq 1.95~$K. Given the current neutrino oscillation measurements, we know most neutrinos move at large, but non-relativistic, velocities. Therefore, dark matter haloes moving in the sea of primordial neutrinos form a neutrino wake behind them, which would slow them down, due to the effect of {\it dynamical friction}. In this paper, we quantify this effect for realistic haloes, in the context of the halo model of structure formation, and show that it scales as $m_\nu^4$ $\times$ relative velocity, and monotonically grows with the halo mass. Galaxy redshift surveys can be sensitive to this effect (at $>3\sigma$ confidence level, depending on survey properties, neutrino mass and hierarchy) through redshift space distortions (RSD) of distinct galaxy populations.