Charting Dark Matter interactions

The nature of Dark Matter (DM) is one of the most compelling problems in Fundamental Physics.It is a well established fact that the Standard Model (SM) of particle physics and General Relativity (GR) by themselves cannot explain astrophysical and cosmological data such as galactic rotation curves, the Cosmic Microwave Background (CMB) and the distribution of structures at large scales.These data indicate the existence of a new fluid, the DM, that is: 1) collisionless 2) cold 3) dominated by GR at large distances.Very few properties are known about the particles making up the DM.The two main ones are: i) the DM must interact weakly with SM particles, and ii) the DM must be stable on cosmological time scales.These two properties by themselves are too general to draw a clear picture of the Dark Sector (DS). In this Thesis we will try to assess some of its properties in light of current and future experiments.The most natural possibility is for the DM to interact with the weakest of the SM forces, the electroweak (EW) force. We completely characterize this kind of DM particles, called WIMPs.After computing their masses, set by EW annihilations, we study their phenomenology at future lepton colliders and at Direct Detection (DD) experiments. The lightest WIMPs are a perfect target for realistic future lepton colliders, while to probe the heaviest ones future Xenon DD experiments are needed.The second scenario we analyze is the case in which DM does not interact with any of the SM force mediators. In this case, the Effective Field Theory (EFT) approach is needed. We introduce a set of portal operators that have received little attention in the past. After describing a model-independent approach, we discuss bounds on the portals coming from high intensity experiments, like neutrino experiments at Fermilab (e.g. DUNE). These are competitive with respect to current constraints.The last possibility is the case in which even portals are absent. In this scenario, the clustering of both species during the Universe evolution can provide a window on the DM nature. We focus on models in which the DM has a long range self-interaction mediated by a light scalar.We study the evolution of inhomogeneities, and compare the predicted CMB anisotropies and galaxy power spectra with current and future data (like Euclid), setting strong bounds on the strength of the self-interaction.Finally we comment on how theoretical insights on DM stability can constrain DM model building.