  Production of Z bosons and neutrinos is studied in the expanding de Sitter
universe. The expression of the transition amplitudes in the case of Z boson
interaction with leptons is established by using perturbative methods. Then the
amplitude and probability for the spontaneous generation from vacuum of a Z
boson a neutrino and an antineutrino are computed analytically and a graphical
analysis is performed in terms of the expansion parameter. We found that the
probability for this process is nonvanishing only for large expansion
conditions of the early Universe. We discuss the Minkowski limit and obtain
that in this limit the amplitude is zero, result which corresponds to the well
established fact that spontaneous particle generation from vacuum in Minkowski
space-time is forbidden by the simultaneous energy and momentum conservation in
perturbative processes. The total probability of the process is computed and we
prove that this quantity is important only for the regime of large expansion
from early universe and is vanishing in the Minkowski limit.
