Constraining Cosmological Parameters Using the Cluster Mass–Richness Relation

Abstract

The cluster mass–richness relation (MRR) is an observationally efficient and potentially powerful cosmological tool for constraining the matter density Ω _m and the amplitude of fluctuations σ _8 using the cluster abundance technique. We derive the MRR relation using GalWCat19 , a publicly available galaxy cluster catalog we created from the Sloan Digital Sky Survey-DR13 spectroscopic data set. In the MRR, cluster mass scales with richness as $\mathrm{log}{M}_{200}=\alpha +\beta \mathrm{log}{N}_{200}$ . We find that the MRR we derive is consistent with both the IllustrisTNG and mini-Uchuu cosmological numerical simulations, with a slope of β ≈ 1. We use the MRR we derived to estimate cluster masses from the GalWCat19 catalog, which we then use to set constraints on Ω _m and σ _8 . Utilizing the all-member MRR, we obtain constraints of Ω _m = ${0.31}_{-0.03}^{+0.04}$ and σ _8 = ${0.82}_{-0.04}^{+0.05}$ , and utilizing the red member MRR only, we obtain Ω _m = ${0.31}_{-0.03}^{+0.04}$ and σ _8 = ${0.81}_{-0.04}^{+0.05}$ . Our constraints on Ω _m and σ _8 are consistent and very competitive with the Planck 2018 results.

Keywords

• Galaxy clusters
• Cosmological parameters
• Galaxy cluster counts