Total probability and number of particles for fermion production in external electric and magnetic fields in de Sitter universe

Abstract

In this paper we present a method for computing the total probability corresponding to the processes of fermion pair production in dipole magnetic field and external Coulomb field in a de Sitter geometry. For that we rewrite the functions that define the amplitudes in terms of oscillatory functions and we use the Taylor expansion of these functions for arriving at the final form of the momenta integrals. The total probability is analysed in terms of the ratio between the mass of the fermion and expansion parameter and we recover the Minkowski limit when the expansion parameter is vanishing. Finally it is proven that from our results we can compute the number of fermions in terms of expansion parameter.