Massive spin-half particle in the de Sitter universe

Abstract

With the use of the Newman-Penrose spin coefficients, the radial part of the electrom equation in the de Sitter-Schwarzschild space is separated, and the transmission coefficient is calculated when the metric is specialized to the de Sitter case. Two different solutions of the radial equation are given. In the first one, the wavenumber corresponds to the flat space value; i.e., k²=ω²−m², where ω is the energy and m is the rest mass of the particle. In this case, when ω»m, the transmission coefficient Γ becomes zero whereas, when ω→m, it is finite and is zero only for the lowest angular momentum state. In the second solution, k² is found to involve the angular momentum. Γ in this case, exhibits a resonance phenomenon and becomes zero only for certain values of the energy or of the mass; one instance when Γ becomes zero is when ω→m, l=½ and k²= m²/4. When m = 0, both expressions for Γ correspond to the value for the massless neutrino.