Non-linear evolution of the cosmic neutrino background

Abstract: We investigate the non-linear evolution of the relic cosmic neutrino background by running large box-size, high resolution N-body simulations. Our set of simulations explore the properties of neutrinos in a reference $\Lambda$CDM model with total neutrino masses between 0.05-0.60 eV in cold dark matter haloes of mass $10^{11}-10^{15}$ $h^{-1}$M$_{\odot}$, over a redshift range $z=0-2$. We compute the halo mass function and show that it is reasonably well fitted by the Sheth-Tormen formula. More importantly, we focus on the CDM and neutrino properties of the density and peculiar velocity fields in the cosmological volume, inside and in the outskirts of virialized haloes. The dynamical state of the neutrino particles depends strongly on their momentum: whereas neutrinos in the low velocity tail behave similarly to CDM particles, neutrinos in the high velocity tail are not affected by the clustering of the underlying CDM component. We find that the neutrino (linear) unperturbed momentum distribution is modified and mass and redshift dependent deviations from the expected Fermi-Dirac distribution are in place both in the cosmological volume and inside haloes. The neutrino density profiles around virialized haloes have been carefully investigated and a simple fitting formula is provided. The neutrino profile, unlike the cold dark matter one, is found to be cored with core size and central density that depend on the neutrino mass, redshift and mass of the halo, for halos of masses larger than $\sim 10^{13.5}h^{-1}$M$_{\odot}$. For lower masses the neutrino profile is best fitted by a simple power-law relation in the range probed by the simulations. Our findings are particularly important in view of upcoming large-scale structure surveys, like Euclid, that are expected to probe the non-linear regime at the percent level with lensing and clustering observations.