Abstract
The problem of the missing mass of the Universe is one of the most puzzling conundrums of modern physics. Assuming that it stems from the existence of yet unknown dark matter (DM) particles, one can probe the cosmos in the hope of detecting unambiguous signatures thereof. The properties of cold DM (CDM) particle candidates lead to the prediction that gravitational structures form on scales much smaller than typical galaxies, below the resolution scope of current cosmological simulations. This clustering translates into a large population of subhalos in galaxies, hence in the Milky Way. Only analytical models can encompass and describe their full distribution. My work is centred upon building a theoretically consistent and dynamically constrained subhalo population model. This relies mostly on three ingredients: the minimal subhalo mass, the cosmological mass function, and dynamical effects. I start from a simplified model of thermally produced dark matter (with scalar, pseudo-scalar, vector and axial-vector interactions with standard model particles). I classify models in terms of small-scale cut-off on the matter power spectrum, which is directly related to the minimal halo mass, making explicit the role of velocity dependence in the interaction processes. Secondly, I improve on the determination of the cosmological subhalo mass function by deriving it from the excursion set theory and a merger tree, while it was previously calibrated on simulations. Thirdly, I incorporate new dynamical effects by analytically studying the impact of stellar encounters susceptible of occurring in galactic discs. Besides, I illustrate an application of this model for indirect detection experiments looking for traces of DM annihilation in the Milky Way. In light of the 1525 unassociated point sources discovered by the Fermi-LAT collaboration, I give prospects for the detection of point-like subhalos as gamma-ray sources with Fermi-LAT-like and CTA-like instruments. I also shortly discuss the impact of additional effects, like the Sommerfeld effect.