Probing the nature of dark matter with small-scale cosmology: A new estimate of the satellite galaxy complement of the Milky Way

The standard model of cosmology has been enormously successful both at reproducing many observed properties of the Universe, and at predicting others. Despite this success one of its key components, a dark matter particle, has not been observed in targeted searches or indirect detection experiments. In addition, a number of discrepancies have arisen between observational proxies of DM structure and the small-scale predictions of this leading cosmological model, challenging its status as the standard paradigm. In this thesis we focus on two distinct but related lines of enquiry. In the first, we address the gap in observational capability concerning the satellite galaxies of the Milky Way. These objects are sensitive probes of the underlying distribution of dark matter, which is determined by the properties of the dark matter particle itself. Using partial observations of the Galactic satellite population, we introduce and use a Bayesian approach to infer the total luminosity function of these objects. We predict that there are $124^{+40}_{-27}$ (68 per cent confidence level) satellite galaxies brighter than ${\rm M}_V=0$ within $300\, {\rm kpc}$ of the Milky Way, and that half of this population should, in principle, be detectable by the forthcoming Large Synoptic Survey Telescope. In the second strand we use these estimates to test the predictions of alternative models to the standard paradigm and place robust lower limits on their allowed properties. We focus on two models of warm dark matter: thermal relics, and sterile neutrinos in the Neutrino Minimal Standard Model ($\nu$MSM). For the former we obtain a robust lower limit on the mass of the dark matter particle, ruling out with 95 per cent confidence models with particle mass, $m_{\rm th}{\leq}1.95\, {\rm keV}$, which is competitive with existing constraints. In the latter case the model depends on the size of the primordial lepton asymmetry, which we parametrize as $L_6$. Assuming a particle mass of $m_{\rm s}=7\, {\rm keV}$—motivated by observations of an unexplained $3.55\, {\rm keV}$ line in X-ray spectra of galaxy clusters—we exclude values of $L_6\geq50$, in agreement with other work