The self-interacting Dirac fields in FLRW spacetime

Abstract

We prove the existence of global in time solution with the small initial data for the semilinear equation of the spin-\(\frac{1}{2}\) particles in the Friedmann–Lemaître–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.