The cluster mass function and the σ8 tension

Abstract

ABSTRACT We use a large set of halo mass function (HMF) models in order to investigate their ability to represent the observational cluster mass function (CMF), derived from the $\tt {GalWCat19}$ cluster catalogue, within the Lambda cold dark matter (ΛCDM) cosmology. We apply the χ2 minimization procedure to constrain the free parameters of the models, namely Ωm and σ8. We find that all HMF models fit well the observational CMF, while the Bocquet et al. model provides the best fit, with the lowest χ2 value. Utilizing the index of inconsistency (IOI) measure, we further test the possible inconsistency of the models with respect to a variety of Planck 2018 ΛCDM cosmologies, resulting from the combination of different probes (CMB–BAO or CMB–DES). We find that the HMF models that fitted well the observed CMF provide consistent cosmological parameters with those of the Planck CMB analysis, except for the Press and Schechter, Yahagi et al., and Despali et al. models that return large IOI values. The inverse $\chi _{\rm min}^2$-weighted average values of Ωm and σ8, overall 23 theoretical HMF models are ${\bar{\Omega }_{m,0}}=0.313\pm 0.022$ and ${\bar{\sigma }_8}=0.798\pm 0.040$, which are clearly consistent with the results of Planck–CMB, providing S8 = σ8(Ωm/0.3)1/2 = 0.815 ± 0.05. Within the ΛCDM paradigm and independently of the selected HMF model in the analysis, we find that the current CMF shows no σ8 tension with the corresponding Planck–CMB results.