Cosmology with massive neutrinos II: on the universality of the halo mass function and bias

We use a large suite of N-body simulations to study departures from universality in halo abundances and clustering in cosmologies with non-vanishing neutrino masses. To this end, we study how the halo mass function and halo bias factors depend on the scaling variable σ²(M,z), the variance of the initial matter fluctuation field, rather than on halo mass M and redshift z themselves. We show that using the variance of the cold dark matter rather than the total mass field, i.e., σ²_cdm(M,z) rather than σ²_m(M,z), yields more universal results. Analysis of halo bias yields similar conclusions: when large-scale halo bias is defined with respect to the cold dark matter power spectrum, the result is both more universal, and less scale- or k-dependent. These results are used extensively in Papers I and III of this series.