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We measure the two-point correlation function (CF) of 1357 galaxy clusters with a mass of log10M200 ≥ 13.6 h−1 M⊙ and at a redshift of z ≤ 0.125. This work differs from previous analyses in that it utilizes a spectroscopic cluster catalogue, $\tt {SDSS-GalWCat}$, to measure the CF and detect the baryon acoustic oscillation (BAO) signal. Unlike previous studies which use statistical techniques, we compute covariance errors directly by generating a set of 1086 galaxy cluster light-cones from the GLAM N-body simulation. Fitting the CF with a power-law model of the form ξ(s) = (s/s0)−γ, we determine the best-fitting correlation length and power-law index at three mass thresholds. We find that the correlation length increases with increasing the mass threshold while the power-law index is almost constant. For log10M200 ≥ 13.6 h−1 M⊙, we find s0 = 14.54 ± 0.87 h−1 Mpc and γ = 1.97 ± 0.11. We detect the BAO signal at s = 100 h−1 Mpc with a significance of 1.60σ. Fitting the CF with a Lambda cold dark matter model, we find $D_\mathrm{V}(z = 0.089)\mathit{r}^{\mathrm{ fid}}_\mathrm{ d}/\mathit{r}_\mathrm{ d} = 267.62 \pm 26$ h−1 Mpc, consistent with Planck 2015 cosmology. We present a set of 108 high-fidelity simulated galaxy cluster light-cones from the high-resolution Uchuu N-body simulation, employed for methodological validation. We find DV(z = 0.089)/rd = 2.666 ± 0.129, indicating that our method does not introduce any bias in the parameter estimation for this small sample of galaxy clusters.

The cluster mass–richness relation (MRR) is an observationally efficient and potentially powerful cosmological tool for constraining the matter density Ω_mand the amplitude of fluctuationsσ₈using the cluster abundance technique. We derive the MRR relation usingGalWCat19, 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$\log M_{200}=\alpha +\beta \log N_{200}$. We find that the MRR we derive is consistent with both the IllustrisTNG and mini-Uchuu cosmological numerical simulations, with a slope ofβ≈ 1. We use the MRR we derived to estimate cluster masses from theGalWCat19catalog, which we then use to set constraints on Ω_mandσ₈. Utilizing the all-member MRR, we obtain constraints of Ω_m=${0.31}_{-0.03}^{+0.04}$andσ₈=${0.82}_{-0.04}^{+0.05}$, and utilizing the red member MRR only, we obtain Ω_m=${0.31}_{-0.03}^{+0.04}$andσ₈=${0.81}_{-0.04}^{+0.05}$. Our constraints on Ω_mandσ₈are consistent and very competitive with the Planck 2018 results.

We report the discovery of MAGAZ3NE J095924+022537, a spectroscopically confirmed protocluster at$z={3.3665}_{-0.0012}^{+0.0009}$around a spectroscopically confirmedUVJ-quiescent ultramassive galaxy (UMG;$M_{\star }={2.34}_{-0.34}^{+0.23}\times {10}^{11}{M}_{\odot }$) in the COSMOS UltraVISTA field. We present a total of 38 protocluster members (14 spectroscopic and 24 photometric), including the UMG. Notably, and in marked contrast to protoclusters previously reported at this epoch that have been found to contain predominantly star-forming members, we measure an elevated fraction of quiescent galaxies relative to the coeval field (${73.3}_{-16.9}^{+26.7}\mathrm{\%}$versus${11.6}_{-4.9}^{+7.1}\mathrm{\%}$for galaxies with stellar massM_⋆≥ 10¹¹M_⊙). This high quenched fraction provides a striking and important counterexample to the seeming ubiquitousness of star-forming galaxies in protoclusters atz> 2 and suggests, rather, that protoclusters exist in a diversity of evolutionary states in the early universe. We discuss the possibility that we might be observing either “early mass quenching” or nonclassical “environmental quenching.” We also present the discovery of MAGAZ3NE J100028+023349, a second spectroscopically confirmed protocluster, at a very similar redshift of$z={3.3801}_{-0.0281}^{+0.0213}$. We present a total of 20 protocluster members, 12 of which are photometric and eight spectroscopic including a poststarburst UMG ($M_{\star }={2.95}_{-0.20}^{+0.21}\times {10}^{11}{M}_{\odot }$). Protoclusters MAGAZ3NE J0959 and MAGAZ3NE J1000 are separated by 18′ on the sky (35 comoving Mpc), in good agreement with predictions from simulations for the size of “Coma”-type cluster progenitors at this epoch. It is highly likely that the two UMGs are the progenitors of Brightest Cluster Galaxies seen in massive virialized clusters at lower redshift.