Cosmic voids are a promising environment to characterize neutrino-induced effects on the large-scale distribution of matter in the universe. We perform a comprehensive numerical study of the statistical properties of voids, identified both in the mat
ter and galaxy distributions, in massive and massless neutrino cosmologies. The matter density field is obtained by running several independent $N$-body simulations with cold dark matter and neutrino particles, while the galaxy catalogs are modeled by populating the dark matter halos in simulations via a halo occupation distribution (HOD) model to reproduce the clustering properties observed by the Sloan Digital Sky Survey (SDSS) II Data Release 7. We focus on the impact of massive neutrinos on the following void statistical properties: number density, ellipticities, two-point statistics, density and velocity profiles. Considering the matter density field, we find that voids in massive neutrino cosmologies are less evolved than those in the corresponding massless neutrinos case: there is a larger number of small voids and a smaller number of large ones, their profiles are less evacuated, and they present a lower wall at the edge. Moreover, the degeneracy between $sigma_8$ and $Omega_{ u}$ is broken when looking at void properties. In terms of the galaxy density field, we find that differences among cosmologies are difficult to detect because of the small number of galaxy voids in the simulations. Differences are instead present when looking at the matter density and velocity profiles around these voids.
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 sim
ulations that incorporate massive neutrinos. Our neutrino halo model is able to capture the non-linear behavior of matter clustering with a $sim 20%$ 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 $sim$ 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.
