Cosmological Constraint on ${\Omega }_m$ and ${\sigma }_8$ from Cluster Abundances using the $GalWCat19$ Optical-Spectroscopic SDSS Catalog

Abstract

We derive cosmological constraints on the matter density, \om, and the amplitude of fluctuations, \sig, using $GalWCat19$, 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 $0.045\le z\le 0.125$ and virial masses of $M\ge 0.8\times 10^{14}$ \hm ~with mean redshift of $z=0.085$, we obtain \om ~$=0.310_{-0.027}^{+0.023}\pm 0.041$ (systematic) and \sig ~$=0.810_{-0.036}^{+0.031}\pm 0.035$ (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 $GalWCat19$ 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 ~$=0.315_{-0.011}^{+0.013}$ and \sig ~$=0.810_{-0.010}^{+0.011}$.

arXiv comment14 pages, 10 figures, accepted for publication in the ApJ

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