Illuminating and Tabulating the Galaxy-Halo Connection

In the near future, a new generation of massively multiplexed spectroscopic surveys like PFS, WAVES, and MOONS will enable detailed studies of galaxy evolution across cosmic timescales and connect galaxies to dark matter halos. I have generated realistic high-redshift mock catalogs for each of these three planned surveys to help quantify and optimize their scientific output. This uses a procedure I developed called Calibrating Light: Illuminating Mocks By Empirical Relations (CLIMBER), and is based on the UniverseMachine model and UltraVISTA photometry. I have compared different targeting strategies by varying the area and targeting completeness and quantified how these survey parameters affect the uncertainty of the two-point correlation function. Through mock observations, I have demonstrated that future extensions of the PFS and MOONS programs should primarily aim to reduce cosmic variance by surveying more uncorrelated sky areas. Additionally, I developed the galtab algorithm to enhance the efficiency of HOD inference by pretabulating populations of galaxies in simulated halo catalogs for rapid, quasi-deterministic estimation of counts-in-cells statistics. This methodology allows posterior probability distributions from Markov chains to converge much more quickly by reducing the required number of trial points by up to an order of magnitude, in addition to enabling even more drastic speedups due to its GPU portability. Leveraging early data from DESI, I have explored the galaxy-halo connection by supplementing number density and the two-point correlation function with galtab-accelerated counts-in-cylinders. My analysis tightly constrains characteristic halo masses and provides strong statistical evidence for positive assembly bias between the r-band luminosity and the halo concentration with up to 3σ significance. Looking ahead, as new methodologies and datasets continue to facilitate our understanding, I anticipate that future studies will soon shift their focus from mere detections of assembly bias to delving into its implications for galaxy formation and cosmology at greater depth