Early Universe production of $W$ bosons in neutrino decays

In this paper we study, via perturbative methods, the rates of production of $W$ bosons emitted in neutrino decays during the early stages of the Universe. We compute the transition amplitude corresponding to the first order of de Sitter electro-weak perturbation theory and study its various limiting cases. The transition rates are derived using minimal subtraction and dimensional regularization. In the end we obtain the density number of bosons (as a function of temperature), and give an estimation of this number for different temperatures and fixed values of the particle momenta.