Constraining Cosmological Parameters Using the Cluster Mass–Richness Relation

Abstract

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 log M 200 = α + β 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 Ωm and σ 8. Utilizing the all-member MRR, we obtain constraints of Ωm = 0.31 − 0.03 + 0.04 and σ 8 = 0.82 − 0.04 + 0.05 , and utilizing the red member MRR only, we obtain Ωm = 0.31 − 0.03 + 0.04 and σ 8 = 0.81 − 0.04 + 0.05 . Our constraints on Ωm and σ 8 are consistent and very competitive with the Planck 2018 results.