  We prove the existence of global in time solution with the small initial data
for the semilinear equation of the spin-1/2 particles in the
Friedmann-Lemaitre-Robertson-Walker spacetime. Moreover, we also prove that if
the initial function satisfies the Lochak-Majorana condition, then the global
solution exists for arbitrary large initial value. The solution scatters to
free solution for large time. The mass term is assumed to be complex-valued.
The conditions on the imaginary part of mass are discussed by proving
nonexistence of the global solutions if certain relation between scale function
and the mass are fulfilled.
