# Perturbative approach to the problem of particle production in electric field on de Sitter universe

## TL;DR

This paper investigates scalar particle production in an external electric field within de Sitter space, revealing directional dependence and conditions for maximum probability, with a focus on a perturbative approach and the Minkowski limit.

## Contribution

It introduces a perturbative method to analyze particle production in de Sitter space under electric fields, emphasizing directional effects and the transition to Minkowski spacetime.

## Key findings

- Probability depends on emission direction.
- Maximum probability occurs along the electric field direction.
- Probability vanishes in the Minkowski limit.

## Abstract

In this letter we study the problem of scalar particle production in external electric field in de Sitter geometry. The total probability is calculated using the previously obtained result in Ref.\cite{6} for transition amplitude in external electric field on de Sitter space. Then we make a graphical study of the total probability in terms of the ratio mass of the particle/expansion factor. Our results show that the probability depend of the direction in which the particles are emitted and that the probability becomes maxim when particles are emitted on the direction of the electric field. In the Minkowski limit we obtain that the probability is vanishing.