Our Universe is puzzling. According to the canonical cosmological model, the Lambda Cold Dark Matter (LCDM) model, around 95\% of the Universe consists of unknown dark matter and dark energy. Despite the unknown nature of these forms of matter and energy, LCDM provides accurate predictions for a variety of observations. One of the main cosmological pillars is the large-scale distribution of galaxies and the underlying dark matter halos, as probed by surveys like The Dark Energy Spectroscopic Instrument (DESI). This Thesis aims to understand the structure and properties of dark matter halos and apply innovative techniques to test the LCDM cosmological paradigm with state-of-the-art surveys like DESI. First, I will show how various halo properties (e.g., halo mass and mass accretion rate) can be inferred from weak lensing observations of cluster-sized halos. Moreover, I will talk about the splashback feature -- a distinct drop in mass density beyond the virial radius predicted by simulations -- and the accuracy and precision with which we can detect it in real data. Finally, I will demonstrate how the most massive galaxies in the Universe present an excellent avenue for performing precision cosmology with DESI. As we enter the era of DESI, millions of galaxies in the nearby Universe will be complete down to 11.5 solar masses. I will show how this dataset will constrain key cosmological parameters while also minimizing systematics plaguing current studies.

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.

Although we have yet to fully understand the nature of dark matter (DM), astrophysical observations across the electromagnetic spectrum allow us to probe its properties and constrain proposed models. These include annihilating DM models that can be investigated through their standard model annihilation products such as electrons and positrons that produce radio, X-ray, and gamma-ray emission through typical radiative processes such as synchrotron radiation and inverse compton scattering. Some other proposed DM models exhibit collisional self interactions that impact the shapes of DM haloes. Using X-ray observations, the DM halo shapes can be constrained in order to probe the strength of possible DM self interactions. In this dissertation, I present an overview of our work in the development of the RX-DMFIT tool to study the secondary emission from DM annihilation, along with applications to DM and cosmic ray studies in the Andromeda galaxy. I also discuss work using data from Chandra and XMM-Newton in studying the X-ray shapes of elliptical galaxies to constrain DM self interactions.

In this dissertation, we describe a calibration and diagnostic framework called Balrog which was used to directly sample the selection and photometric biases of the Dark Energy Survey (DES) Year 3 (Y3) dataset. We systematically inject onto the single-epoch images of a random 20% subset of the DES footprint an ensemble of nearly 30 million realistic galaxy models derived from DES Deep Field observations. These augmented images are analyzed in parallel with the original data to automatically inherit measurement systematics that are often too difficult to capture with traditional generative models. The resulting object catalog is a Monte Carlo sampling of the DES transfer function and is used as a powerful diagnostic and calibration tool for a variety of DES Y3 science, particularly for the calibration of the photometric redshifts of distant "source" galaxies and magnification biases of nearer "lens" galaxies. The recovered Balrog injections are shown to closely match the photometric property distributions of the fiducial Y3 GOLD catalog, particularly in color, and capture the number density fluctuations from observing conditions of the real data within 1% for a typical galaxy sample. We find that Y3 colors are extremely well calibrated, typically within ~1-8 millimagnitudes, but for a small subset of objects we detect significant magnitude biases correlated with large overestimates of the injected object size due to proximity effects and blending. Finally, we discuss approaches to extend the current methodology to capture more aspects of the transfer function for future analyses.