Constraining Cosmological Parameters Using the Cluster Mass-Richness Relation

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.