Baryon asymmetry of the Universe without Boltzmann or Kadanoff-Baym equations

We present a formalism that allows the computation of the baryon asymmetry of the Universe, from the first principles of statistical physics and quantum field theory, that is applicable to certain types of physics beyond the standard model (such as the neutrino minimal standard model) and does not require the solution of Boltzmann or Kadanoff-Baym equations. The formalism works if a thermal bath of standard model particles is very weakly coupled to a new sector (sterile neutrinos in the neutrino minimal standard model case) that is out-of-equilibrium. The key point that allows a computation without kinetic equations is that the number of sterile neutrinos produced during the relevant cosmological period remains small. In such a case, it is possible to expand the formal solution of the von Neumann equation perturbatively and obtain a master formula for the lepton asymmetry expressed in terms of nonequilibrium Wightman functions. The master formula neatly separates CP-violating contributions from finite temperature correlation functions and satisfies all three Sakharov conditions. These correlation functions can then be evaluated perturbatively; the validity of the perturbative expansion depends on the parameters of the model considered. Here, we choose a toy model (containing only two active and two sterile neutrinos) to illustrate the use of the formalism, but it could be applied to other models.