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

## TL;DR

This paper develops a method to compute fermion pair production probabilities in external fields within a de Sitter universe, analyzing how these probabilities depend on fermion mass and expansion rate, and deriving fermion counts.

## Contribution

Introduces a novel approach for calculating fermion production probabilities and number of particles in de Sitter space with external fields, linking to Minkowski limit.

## Key findings

- Total probability depends on fermion mass and expansion parameter.
- Method recovers Minkowski space results when expansion vanishes.
- Allows computation of fermion number from probability 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.