Why is there more matter than antimatter? Calculational methods for leptogenesis and electroweak baryogenesis

We review the production of the matter–antimatter asymmetry in the early Universe, that is baryogenesis, in out-of-equilibrium conditions induced by decays of heavy particles or by the presence of phase boundaries. The most prominent examples are given by leptogenesis and electroweak baryogenesis, respectively. For both cases, we derive the equations that govern the production of the asymmetries. We first use intuitive arguments based on classical fluid equations in combination with quantum-field-theoretical effects of CP-violation. As for a more thorough approach that is well-suited for systematic improvements, we obtain the real-time evolution of the system of interest using the closed time-path method. We thus provide a simple and practicable scheme to set up phenomenological fluid equations based on first principles of quantum field theory. Necessary for baryogenesis are both, CP even as well as odd phases in the amplitudes. A possibility of generating the even phases is the coherent superposition of quantum states, i.e. mixing. These coherence effects are essential in resonant leptogenesis as well as in some scenarios of electroweak baryogenesis. Recent theoretical progress on asymmetries from out-of-equilibrium decays may therefore also be applicable to baryogenesis at phase boundaries.