| The advent of large and overlapping sky surveys brings promise of a new era in the study of galaxy clusters and dark energy. Clusters have been used for decades as faithful buoys of space-time, tracing cosmic evolution through their matter content and spatial distribution. High-fidelity tracking relies on a robust connection between observable cluster signatures and the underlying dark matter content, which is otherwise invisible. Until now, clusters have been mostly viewed through independent signals in distinct wavebands. The next era of cluster cosmology may be led by multi-variate, cross-waveband detections and analyses of clusters, where different facets of clusters can be cross-correlated to develop a more complete, unified picture of cluster populations. To these ends, in this dissertation, I perform multi-variate analyses of galaxy cluster populations and develop a simulated sky survey, with which to prepare for the next generation of multi-wavelength cluster observations. First, in a new multi-variate framework, I quantify the effects of observational biases on measures of the cluster distribution function and on cosmological constraints derived from X-ray cluster populations. I also demonstrate the indispensability of the multi-variate approach in measuring the evolution of X-ray galaxy clusters; without it, we find that the combination of scatter, intrinsic correlation and irrevocable survey flux limits substantially confuses any measure of redshift evolution. Next, I construct the Millennium Gas Simulation-Virtual Sky Survey (MGSVSS), a multi-wavelength mock sky derived from an N-body gas-dynamic simulation. The MGSVSS contains both sub-mm and optical wavelength sky signals to redshift, z = 1., in a 5 x 5deg2 field of view, with O (103) halos, O (104) optically selected clusters, and O (102) clusters selected via the Sunyaev-Zel'dovich (SZ) signature. The SZ sky also includes a minimal level of sky and instrumental noise, which nearly mimics that of modern SZ cluster surveys. I have performed cluster-finding in the optical and sub-mm wavebands (independently) and obtained a scaling relation between the SZ decrement and the optical richness of independently observed clusters. In this preliminary exercise, I begin to address issues regarding SZ-optical cross-correlation and the optimization of cluster-finding methods toward both cross-correlation and joint finding. |
