We derive cosmological constraints on the matter density, \om, and the amplitude of fluctuations, \sig, using $\mathtt{GalWCat19}$, a catalog of 1800 galaxy clusters we identified in the Sloan Digital Sky Survey-DR13 spectroscopic data set using our GalWeight technique to determine cluster membership \citep{Abdullah18,Abdullah19}. By analyzing a subsample of 756 clusters in a redshift range of $0.045\leq z \leq 0.125$ and virial masses of $M\geq 0.8\times10^{14}$ \hm ~with mean redshift of $z = 0.085$, we obtain \om ~$=0.310^{+0.023}_{-0.027} \pm 0.041$ (systematic) and \sig ~$=0.810^{+0.031}_{-0.036}\pm 0.035$ (systematic), with a cluster normalization relation of $\sigma_8= 0.43 \Omega_m^{-0.55}$. There are several unique aspects to our approach: we use the largest spectroscopic data set currently available, and we assign membership using the GalWeight technique which we have shown to be very effective at simultaneously maximizing the number of {\it{bona fide}} cluster members while minimizing the number of contaminating interlopers. Moreover, rather than employing scaling relations, we calculate cluster masses individually using the virial mass estimator. Since $\mathtt{GalWCat19}$ is a low-redshift cluster catalog we do not need to make any assumptions about evolution either in cosmological parameters or in the properties of the clusters themselves. Our constraints on \om ~and \sig ~are consistent and very competitive with those obtained from non-cluster abundance cosmological probes such as Cosmic Microwave Background (CMB), Baryonic Acoustic Oscillation (BAO), and supernovae (SNe). The joint analysis of our cluster data with Planck18+BAO+Pantheon gives \om ~$=0.315^{+0.013}_{-0.011}$ and \sig ~$=0.810^{+0.011}_{-0.010}$.

中文翻译：

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使用 GalWCat19 光谱 SDSS 目录对 Ω m 和 σ 8 的宇宙学约束来自簇丰度

我们使用 $\mathtt{GalWCat19}$ 推导出对物质密度 \om 和波动幅度 \sig 的宇宙学约束，这是我们在斯隆数字巡天-DR13 光谱数据集中识别的 1800 个星系团的目录，使用我们的 GalWeight 技术来确定集群成员 \citep{Abdullah18,Abdullah19}。通过分析红移范围为 $0.045\leq z \leq 0.125$ 的 756 个簇的子样本和 $M\geq 0.8\times10^{14}$ \hm ~ 平均红移 $z = 0.085$，我们获得 \om ~$=0.310^{+0.023}_{-0.027} \pm 0.041$（系统的）和 \sig ~$=0.810^{+0.031}_{-0.036}\pm 0.035$（系统的），与$\sigma_8= 0.43 \Omega_m^{-0.55}$ 的聚类归一化关系。我们的方法有几个独特的方面：我们使用目前可用的最大光谱数据集，我们使用 GalWeight 技术分配成员资格，我们已经证明该技术非常有效地同时最大化 {\it{bona fide}} 集群成员的数量，同时最小化污染闯入者的数量。此外，我们不使用比例关系，而是使用维里质量估计器单独计算集群质量。由于 $\mathtt{GalWCat19}$ 是一个低红移的星团目录，我们不需要对宇宙学参数或星团本身的属性做出任何关于演化的假设。我们对 \om ~ 和 \sig ~ 的约束与从非星团丰度宇宙学探测器（如宇宙微波背景 (CMB)、重子声波振荡 (BAO) 和超新星 (SNe)）获得的约束一致且极具竞争力。