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 sigma(2) (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., sigma(2)(cdm) (M, z) rather than sigma(2)(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.