The halo model in a massive neutrino cosmology

We provide a quantitative analysis of the halo model in the context of massive neutrino cosmologies. We discuss all the ingredients necessary to model the non-linear matter and cold dark matter power spectra and compare with the results of N-body simulations that incorporate massive neutrinos. Our neutrino halo model is able to capture the non-linear behavior of matter clustering with a 20\% accuracy up to very non-linear scales of k=10~h/Mpc (which would be affected by baryon physics). The largest discrepancies arise in the range k=0. 5-1~h/Mpc where the 1-halo and 2-halo terms are comparable and are present also in a massless neutrino cosmology. However, at scales k<0. 2~h/Mpc our neutrino halo model agrees with the results of N-body simulations at the level of 8\% for total neutrino masses of <0. 3 eV. We also model the neutrino non-linear density field as a sum of a linear and clustered component and predict the neutrino power spectrum and the cold dark matter-neutrino cross-power spectrum up to k=1~h/Mpc with 30\% accuracy. For masses below 0. 15 eV the neutrino halo model captures the neutrino induced suppression, casted in terms of matter power ratios between massive and massless scenarios, with a 2\% agreement with the results of N-body/neutrino simulations. Finally, we provide a simple application of the halo model: the computation of the clustering of galaxies, in massless and massive neutrinos cosmologies, using a simple Halo Occupation Distribution scheme and our halo model extension.