Global in time self-interacting Dirac fields in the de Sitter space

TL;DR

This paper investigates the existence and blow-up conditions of global solutions for self-interacting Dirac fields in de Sitter space, considering small and large initial data and the effect of the Hubble constant.

Contribution

It establishes the existence of global solutions for semilinear Dirac equations in de Sitter space under various conditions, including large data and specific physical constraints.

Findings

Existence of global small data solutions in de Sitter space.

Existence of global large data solutions under Lochak-Majorana condition.

Finite time blow-up conditions depending on initial data and spacetime parameters.

Abstract

In this paper the semilinear equation of the spin-$\frac{1}{2}$ fields in the de Sitter space is investigated. We prove the existence of the global in time small data solution in the expanding de Sitter universe. Then, under the Lochak-Majorana condition, we prove the existence of the global in time solution with large data. The sufficient conditions for the solutions to blow up in finite time are given for large data in the expanding and contracting de Sitter spacetimes. The influence of the Hubble constant on the lifespan is estimated.