Modeling the distribution of dark matter and its connection to galaxies

Despite the mysterious nature of dark matter and dark energy, the Lambda-Cold Dark Matter (LCDM) model provides a reasonably accurate description of the evolution of the cosmos and the distribution of galaxies. Today, we are set to tackle more specific and quantitative questions about the galaxy formation physics, the nature of dark matter, and the connection between the dark and the visible components. The answers to these questions are however elusive, because dark matter is not directly observable, and various unknowns lie between what we can observe and what we can calculate. Hence, mathematical models that bridge the observable and the calculable are essential for the study of modern cosmology. The aim of my thesis work is to improve existing models and also to construct new models for various aspects of the dark matter distribution, as dark matter structures the cosmic web and forms the nests of visible galaxies. Utilizing a series of cosmological dark matter simulations which span a wide dynamical range and a statistical sample of zoom-in simulations which focus on individual dark matter halos, we develop models for the spatial and velocity distribution of dark matter particles, the abundance of dark substructures, and the empirical connection between dark matter and galaxies. As more precise observational results become available, more accurate models are then required to test the consistency between these results and the LCDM predictions. For all the models we investigate, we find that the formation history of dark matter halos always plays a crucial role. Neglecting the halo formation history would result in systematic biases when we interpret various observational results, including dark matter direct detection experiments, the detection of dark substructures with strong-lensed systems, the large-scale spatial clustering of galaxies, and the abundance of dwarf galaxies. Rectifying this, our work will enable us to fully utilize the complementary power of diverse observational datasets to test the LCDM model and to seek new physics.