Dynamics of phase transitions in the early universe and cosmological consequences

The advent of gravitational waves (GW) astronomy opens the possibility of probing experimentally the first second of the universe. As a consequence, having a theoretical control over all the early universe events that may have occurred and the putative GW signal that would have been produced at those events has become an urgent matter. The main aim of this thesis is to study the dynamics of First Order Phase Transition (FOPT) with relativistic bubble walls in correlation with the three following processes: GW emission, baryogenesis and production of Dark Matter (DM). After recalling the basics of cosmology, of thermal field theory and of FOPTs in the early universe in the first chapter, in the second chapter, we discuss at length the pressure on the domain wall of the bubble in the ultra-relativistic limit. In so doing we identify and discuss in depth three contributions to this pressure: from particles gaining a mass in the transition, from heavy states with mass up to $\sqrt{\gamma_w v_{\rm trans} T_{\rm nuc}}$ emitted during the transition, and from the emission of ultra-soft gauge bosons obtaining a mass in the transition. We subsequently apply those results to find the full pressure in the case of a generic PT and in the case of the ElectroWeak Phase Transition (EWPT). In a third chapter, we come back to the process of production of heavy states and we show that those heavy states, once produced, can be stable and constitute a viable super-heavy DM candidate. We study the relic abundance matching observations in the context of dark PT (by dark we mean a transition which is neither EWPT neither QCDPT) and in the context of the EWPT. In the fourth chapter, we complete the study of the production of heavy states by going to one-loop level. We show that if an imaginary phase is present in the Yukawa matrix, CP-violation can occur in the process of production, opening a possible route for baryogenesis. As a proof of principle, we then provide two different models realising baryogenesis via relativistic bubble walls. The first model uses the breaking of the $U_L(1)$ lepton number during a dark PT at high scale to generate relativistic walls and baryogenesis. The second model postulates a heavy extension of the standard model (SM) with new source of CP and baryon number breaking and a strong EWPT with relativistic EW bubble wall to induce baryogenesis. In all our models we left the phase transition sector as an unknown, only assuming that the wall would become ultra-relativistic.