Galaxy cluster number count data constraints on cosmological parameters

Understand

[Abridged] We use data on massive galaxy clusters ($M_{\rm cluster} > 8 \times 10^{14} h^{-1} M_\odot$ within a comoving radius of $R_{\rm cluster} = 1.5 h^{-1}\Mpc$) in the redshift range $0.05 \lesssim z \lesssim 0.83$ to place constraints, simultaneously, on the nonrelativistic matter density parameter $\Omega_m$, on the amplitude of mass fluctuations $\sigma_8$, on the index $n$ of the power-law spectrum of the density perturbations, and on the Hubble constant $H_0$, as well as on the equation-of-state parameters $(w_0,w_a)$ of a smooth dark energy component.

• For the first time, we properly take into account the dependence on redshift and cosmology of the quantities related to cluster physics: the critical density contrast, the growth factor, the mass conversion factor, the virial overdensity, the virial radius and, most importantly, the cluster number count derived from the observational temperature data.
• We show that, contrary to previous analyses, cluster data alone prefer low values of the amplitude of mass fluctuations, $\sigma_8 \leq 0.69 (1\sigma C.L.)$, and large amounts of nonrelativistic matter, $\Omega_m \geq 0.38 (1\sigma C.L.)$, in slight tension with the $\Lambda$CDM concordance cosmological model, though the results are compatible with $\Lambda$CDM at $2\sigma$.
• In addition, we derive a $\sigma_8$ normalization relation, $\sigma_8 \Omega_m^{1/3} = 0.49 \pm 0.06 (2\sigma C.L.)$.