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 electroweak perturbation theory and study its various limiting cases. The transition rates are derived using minimal subtraction and dimensional regularization. In the end we attempt to obtain the density number of $W$ bosons produced in perturbative transitions in de Sitter spacetime, using the rates obtained in this paper and in previous ones, and analyze the density number with respect to the particle momenta and renormalisation mass $\mu$.