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In this paper we study the charged electro-weak interactions in the de Sittergeometry. We develop the reduction formalism for the Proca field with the helpof the solutions for the interacting fields. Perturbation theory is used forobtaining the definition of the transition amplitudes in the first order. Weapply our formalism to the study of spontaneous vacuum emission of fermions,anti-fermions and $W^{\pm}$ bosons in the expanding de Sitter universe. Ourresults are generalizations of the Weinberg-Salam electro-weak theory to curvedspace-time, in the case of $W^{\pm}$ boson interaction with leptons. Theprobability and transition amplitude are found to be a quantities which dependon the Hubble parameter. Our analytical and graphical results prove that suchperturbative processes are possible only for the large expansion conditions ofthe early Universe. The total probability and rate of transition are obtainedfor the case of large expansion and we use dimensional regularization andPauli-Villars regularization for the momenta integrals. In the end we recoverthe Minkowski limit, where our probabilities vanish, thus confirming the wellknown fact that spontaneous vacuum emission of $W^{\pm}$ bosons and fermions isforbidden in flat space-time due to energy-momentum conservation.

Production of massive $W^{\pm}$ bosons and fermion-antifermion pairs from vacuum in the de Sitter Universe