Cosmological Constraints on Ωm and σ8 from Cluster Abundances Using the GalWCat19 Optical-spectroscopic SDSS Catalog

We derive cosmological constraints on the matter density, ${{\rm{\Omega }}}_{m}$ , and the amplitude of fluctuations, ${\sigma }_{8}$ , using ${\mathtt{GalWCat}}{\mathtt{19}}$ , 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. By analyzing a subsample of 756 clusters in a redshift range of 0.045 ≤ z ≤ 0.125 and virial masses of M ≥ 0.8 × 10¹⁴ ${h}^{-1}\ {M}_{\odot }$ with mean redshift of z = 0.085, we obtain ${{\rm{\Omega }}}_{m}={0.310}_{-0.027}^{+0.023}\pm 0.041$ (systematic) and ${\sigma }_{8}={0.810}_{-0.036}^{+0.031}\pm 0.035$ (systematic), with a cluster normalization relation of ${\sigma }_{8}=0.43{{\rm{\Omega }}}_{m}^{-0.55}$ . 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 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 ${\mathtt{GalWCat}}{\mathtt{19}}$ 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 ${{\rm{\Omega }}}_{m}$ and ${\sigma }_{8}$ are consistent and very competitive with those obtained from non-cluster abundance cosmological probes such as cosmic microwave background, baryonic acoustic oscillation (BAO), and supernovae. The joint analysis of our cluster data with Planck18+BAO+Pantheon gives ${{\rm{\Omega }}}_{m}={0.315}_{-0.011}^{+0.013}$ and ${\sigma }_{8}={0.810}_{-0.010}^{+0.011}$ .