The formation history of galaxy clusters is a powerful probe of cosmology. In particular, one may place strong constraints on the dark energy equation of state by examining the evolution across redshift of the number density of galaxy clusters as a function of mass. In this thesis, I describe my contributions to cluster cosmology, in particular to the development of the richness optical observable mass proxy.
I introduce redMaPPer, an optical cluster finder which represents an important upstream input for my thesis work. I next introduce the Mass Analysis Tool for Chandra (MATCha), a pipeline which uses a parallelized algorithm to analyze archival Chandra data. MATCha simultaneously calculates X-ray temperatures and luminosities and performs centering measurements for hundreds of potential galaxy clusters using archival X-ray exposures. I run MATCha on the redMaPPer SDSS DR8 cluster catalog and use MATCha's output X-ray temperatures and luminosities to analyze the galaxy cluster temperature-richness, luminosity-richness, luminosity-temperature, and temperature-luminosity scaling relations. I investigate the distribution of offsets between the X-ray center and redMaPPer center within 0.1 < z < 0.35 and explore some of the causes of redMaPPer miscentering. I collaborate with members of the Dark Energy Survey in order to repeat this analysis on Dark Energy Survey Year 1 data. I outline the various ways in which MATCha constitutes an important upstream work for a variety of astrophysical applications. These include the calibrations of two separate mass proxies, the study of the AGN fraction of galaxy clusters, and cosmology from cluster number densities and stacked weak lensing masses. Finally, I outline future upgrades and applications for MATCha throughout the lifespan of the Dark Energy Survey and the Large Synoptic Survey Telescope.