# Schwinger Pair Production by Electric Field Coupled to Inflaton

## TL;DR

This paper analytically studies Schwinger pair production in de Sitter space with an electric field, revealing how the nature of turning points affects particle production and electric current, especially in weak field regimes.

## Contribution

It introduces an analytical approach using uniform asymptotic approximation to analyze how different parameter regimes influence Schwinger pair production in curved spacetime.

## Key findings

- Complex turning points suppress electric current when β > 0.
- Real turning points facilitate particle production, especially for negative β.
- Electric current scales as E^{1/2 - sqrt{|β|}} in weak electric fields, enhanced for m < sqrt(2)H.

## Abstract

We analytically investigate the Schwinger pair production in the de Sitter background by using {\em the uniform asymptotic approximation method}, and show that the equation of motion in general has two turning points, and the nature of these points could be single, double, real or complex, depending on the choice of the free parameters involved in the theory. Different natures of these points lead to different electric currents. In particular, when $\beta \equiv m^2/H^2-9/4$ is positive, both turning points are complex, and the electric current due to the Schwinger process is highly suppressed, where $m$ and $H$ denote, respectively, the mass of the particle and the Hubble parameter. For the turning points to be real, it is necessary to have $\beta < 0$, and the more negative of $\beta$, the easier to produce particles. In addition, when $\beta < 0$, we also study the particle production when the electric field $E$ is very weak. We find that the electric current in this case is proportional to $E^{1/2 - \sqrt{|\beta|}}$, which is strongly enhanced in the weak electric field limit when $m < \sqrt{2} H$.