The self-interacting Dirac fields in FLRW spacetime

TL;DR

This paper proves the existence of global solutions for self-interacting Dirac fields in FLRW spacetime, including cases with large initial data under specific conditions, and analyzes scattering and mass-related constraints.

Contribution

It establishes the existence of global solutions for semilinear Dirac equations in FLRW spacetime, including cases with large initial data satisfying the Lochak-Majorana condition, and explores mass-related nonexistence conditions.

Findings

Global solutions exist for small initial data.

Solutions scatter to free solutions at large times.

Mass imaginary part conditions affect solution existence.

Abstract

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.