Dark Matter and gauge dynamics

Many astrophysical and cosmological observations suggest that about 25\% of the Universe is composed by non-baryonic matter that we know as Dark Matter. This experimental evidence requires new physics beyond the Standard Model, which must provide new particles stable on cosmological scales and very weakly interacting with the Standard Model sector. In this Thesis we discuss theories in which gauge dynamics provides accidentally stable Dark Matter candidates. We extend the Standard model with new dark gauge interactions and new fields charged under them. Gauge invariance naturally leads to accidental global symmetries of the Lagrangian, which in turn imply Dark Matter stability, in the same way as the proton stability comes from the accidental conservation of baryon number. In the first part of the Thesis we focus on renormalizable scalar gauge theories: we consider minimal extension of the Standard Model based on a new dark gauge symmetry and one scalar multiplet. Dark Matter is a thermal relic with a typical mass around 100 TeV, usually in the form of a dark baryon or a dark meson. Gauge confinement gives a strong suppression of the cosmological abundance, which is further diluted by the out-of-equilibrium decay of heavy dark glue-balls. We provide predictions for the Dark Matter phenomenology. We explore the different phases of the theory: in the confined phase the dark gauge group becomes strongly coupled and confines; in the Higgs phase the scalar field acquires a vacuum expectation value and the dark gauge group gets spontaneously broken. We claim a duality among the two phases if the scalar field fills the fundamental representation of the dark gauge group. We further extend this framework by adding new heavy fermionic states which provide an accidental and high-quality Peccei-Quinn symmetry and axion Dark Matter. In the second part of the Thesis we propose two models in which gravity plays a fundamental role in the production and/or dynamics of Dark Matter. These are based on non-abelian gauge theories with only gravitational interactions with the Standard Model. Dark Matter is made either by long-lived dark glue-balls produced through gravitational freeze-in or by macroscopic gravitational bound states which emerge form a first order confining phase transition.