Cosmology with massive neutrinos III: The halo mass function and an application to galaxy clusters

We use a suite of N-body simulations that incorporate massive neutrinos as an extra-set of particles to investigate their effect on the halo mass function. We show that for cosmologies with massive neutrinos the mass function of dark matter haloes selected using the spherical overdensity (SO) criterion is well reproduced by the fitting formula of Tinker et al. (2008) once the cold dark matter power spectrum is considered instead of the total matter power, as it is usually done. The differences between the two implementations, i.e. using P cdm(k) instead of Pm(k), are more pronounced for large values of the neutrino masses and in the high end of the halo mass function: in particular, the number of massive haloes is higher when Pcdm(k) is considered rather than Pm(k). As a quantitative application of our findings we consider a Planck-like SZ-clusters survey and show that the differences in predicted number counts can be as large as 30% for ∑m ν = 0.4 eV. Finally, we use the Planck-SZ clusters sample, with an approximate likelihood calculation, to derive Planck-like constraints on cosmological parameters. We find that, in a massive neutrino cosmology, our correction to the halo mass function produces a shift in the σ8(Ωm/0.27)γ relation which can be quantified as Δγ ∼ 0.05 and Δγ ∼ 0.14 assuming one (Nν = 1) or three (Nν = 3) degenerate massive neutrino, respectively. The shift results in a lower mean value of σ8 with Δσ8 = 0.01 for Nν = 1 and Δσ8 = 0.02 for Nν = 3, respectively. Such difference, in a cosmology with massive neutrinos, would increase the tension between cluster abundance and Planck CMB measurements. © 2013 IOP Publishing Ltd and Sissa Medialab srl.