UC Riverside

The dissertation includes three manuscripts. Firstly, we introduce the GalWeight technique, a new technique for assigning galaxy cluster membership. GalWeight is designed to simultaneously maximize the number of {\it bona fide} cluster members while minimizing the number of interlopers. GalWeight can be applied to both massive and poor galaxy groups and is effective in identifying members in both the virial and infall regions with high efficiency. We apply GalWeight to MDPL2 \& Bolshoi N-body simulations, and find that it is $> 98\%$ accurate in correctly assigning cluster membership. We apply GalWeight to a sample of twelve Abell clusters using observations from the Sloan Digital Sky Survey.

Secondly, we apply GalWeight to the SDSS-DR13 spectroscopic data set to create a new publicly-available catalog of 1800 galaxy clusters ($\mathtt{GalWCat19}$) and a corresponding catalog of 34471 identified member galaxies. The clusters are identified from overdensities in redshift-phase space. The cluster masses are calculated using the virial theorem and NFW model. The $\mathtt{GalWCat19}$ clusters range in redshift between $0.01 - 0.2$ and in mass between $(0.4 - 14) \times 10^{14}h^{-1}M_{\odot}$. The cluster catalog provides position, redshift, membership, velocity dispersion, and mass at overdensities $\Delta = 500, 200, 100, 5.5$ for each cluster. The 34471 member galaxies are identified within the radius at overdensity of $\Delta = 200$. The galaxy catalog provides the coordinates of each galaxy and the ID of the cluster that the galaxy belongs to.

Thirdly, we derive cosmological constraints on the matter density, \om, and the amplitude of fluctuations, \sig, using $\mathtt{GalWCat19}$. We investigate the volume and mass incompleteness of $\mathtt{GalWCat19}$ to obtain a complete local subsample of 756 clusters ($\mathtt{SelFMC}$) in a redshift range of $0.045\leq z \leq 0.125$ and virial masses of $M\geq 0.8\times10^{14}$ \hm used to constrain \om ~and \sig. Utilizing $\mathtt{SelFMC}$, 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). Our constraints on \om ~and \sig ~are consistent and very competitive with those obtained from other cosmological probes of 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 ~$=0.810^{+0.011}_{-0.010}$.