  In this paper we study the charged electro-weak interactions in the de Sitter
geometry. We develop the reduction formalism for the Proca field with the help
of the solutions for the interacting fields. Perturbation theory is used for
obtaining the definition of the transition amplitudes in the first order. We
apply our formalism to the study of spontaneous vacuum emission of fermions,
anti-fermions and $W^{\pm}$ bosons in the expanding de Sitter universe. Our
results are generalizations of the Weinberg-Salam electro-weak theory to curved
space-time, in the case of $W^{\pm}$ boson interaction with leptons. The
probability and transition amplitude are found to be a quantities which depend
on the Hubble parameter. Our analytical and graphical results prove that such
perturbative processes are possible only for the large expansion conditions of
the early Universe. The total probability and rate of transition are obtained
for the case of large expansion and we use dimensional regularization and
Pauli-Villars regularization for the momenta integrals. In the end we recover
the Minkowski limit, where our probabilities vanish, thus confirming the well
known fact that spontaneous vacuum emission of $W^{\pm}$ bosons and fermions is
forbidden in flat space-time due to energy-momentum conservation.
