Production of massive spin-1/2 particles in anisotropic spacetimes

Abstract

The author obtains general expressions for the number and energy densities of free, massive spin-1/2 particles produced by quantum effects in a weakly anisotropic spacetime of Bianchi type I. For this purpose they construct solutions of the Dirac equation as perturbation expansions in a quantity describing the deviation from conformal invariance. Thus they generalise a well known perturbation method to massive particles with spin 1/2 and anisotropic spacetime. They consider a few explicit examples for both isotropic and anisotropic expansion and discuss the relevance of the corresponding results for the early universe. These examples allow singularity avoidance and anisotropy damping to be modelled. Particle production effects become significant when the characteristic timescale of the expansion of the universe is comparable with the particle's Compton time. If the universe passes through a singularity the energy densities take their largest values but they remain finite and approach zero exponentially fast in the limit of large particle mass. Anisotropic damped oscillations, the frequency of which is only a few Planck frequencies, have to be damped out within a few Planck times in order to give rise to energy densities of a reasonable order of magnitude.