4.6 Article

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

Journal

Publisher

IOP PUBLISHING LTD
DOI: 10.1088/1475-7516/2013/12/012

Keywords

galaxy clusters; cluster counts; cosmological parameters from LSS; neutrino masses from cosmology

Funding

  1. STFC
  2. Large Facilities Capital Fund of BIS
  3. University of Cambridge
  4. Darwin Supercomputer of the University of Cambridge High Performance Computing Service
  5. Dell Inc. from the Higher Education Funding Council for England
  6. PRIN-INAF09 project
  7. PRIN-MIUR09
  8. PD51 INFN grant
  9. Marie Curie Initial Training Network CosmoComp [PITN-GA-2009-238356]
  10. ERC Starting Grant CosmoIGM
  11. National Youth Thousand Talents Program
  12. NSF-AST [0908241]
  13. [Y25155E0U1]
  14. [Y3291740S3]

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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 P-m(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 P-cdm(k) is considered rather than P-m(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 Sigma m(nu) = 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 sigma(8) (Omega(m)/0.27)(gamma) relation which can be quantified as Delta gamma similar to 0.05 and Delta gamma similar to 0.14 assuming one (N-nu - 1) or three (N-nu = 3) degenerate massive neutrino, respectively. The shift results in a lower mean value of sigma(8) with Delta sigma(8) = 0.01 for N-nu - 1 and Delta sigma(8) - 0.02 for N-nu - 3, respectively. Such difference, in a cosmology with massive neutrinos, would increase the tension between cluster abundance and Planck CMB measurements.

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