Abstract
The cluster mass–richness relation (MRR) is an observationally efficient and potentially powerful cosmological tool for constraining the matter density Ωm 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 . 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 Ωm and σ 8. Utilizing the all-member MRR, we obtain constraints of Ωm = and σ 8 = , and utilizing the red member MRR only, we obtain Ωm = and σ 8 = . Our constraints on Ωm and σ 8 are consistent and very competitive with the Planck 2018 results.
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