Magnetic Catalysis and Fermion Mass Generation in de Sitter Spacetime

Abstract

We consider the dynamics of a charged fermion in de Sitter space in the presence of a uniform background magnetic field, and discuss magnetic catalysis of chiral symmetry breaking using the Nambu--Jona-Lasinio (NJL) model. We evaluate the mode functions of the charged fermion field in this background by imposing the Bunch--Davies vacuum condition. The gap equation is solved in the mean-field approximation. We derive analytic expressions for the gap in several limiting regimes, such as the large-magnetic-field and large-curvature limits. We find that the curvature effect restores chiral symmetry, whereas the magnetic field enhances chiral symmetry breaking through the conventional mechanism of magnetic catalysis. The phase structure associated with chiral symmetry breaking is revealed by numerical calculations.