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Neutrinos are believed to be the most abundant fermions in the Universe, buttheir masses are unknown, except for being non-zero but much smaller than otherfermions. Cosmological relic neutrinos could also have non-zero chemicalpotentials (or asymmetries). We develop a fast neutrino-involved N-bodysimulation code to include both neutrino mass and asymmetry effects. Using it,we investigate the neutrino effects on the matter pairwise velocity, whichitself is an interesting probe of cosmology. We find that for light-halo($[10^{11},10^{13}]\ M_\odot$) mean pairwise velocity, in the transition range($[4,15]\ \mathrm{Mpc}$), the effects of neutrino masses overwhelm the effectsof neutrino asymmetries, while in the two-halo-group range ($[25,50]\\mathrm{Mpc}$), for both light and heavy haloes ($[10^{13},10^{15}]\ M_\odot$),the effects of neutrino asymmetries dominate, making it possible to disentanglethe two effects. We provide fitting formulae to quantify the effects ofneutrino mass and asymmetry on halo-halo pairwise velocities.

Measuring neutrino mass and asymmetry with matter pairwise velocities