# Generalized Schwinger effect and particle production in an expanding universe

## TL;DR

This paper explores particle production in expanding universes and electric fields, establishing a mathematical link between the two, and analyzing combined effects, non-analytic behaviors, and vacuum definitions in such dynamic backgrounds.

## Contribution

It introduces an algebraic mapping connecting particle production in electric fields and expanding universes, and investigates combined effects and non-analytic behaviors.

## Key findings

- Derived a mapping between electric field and expanding universe equations
- Identified conditions for Planck spectrum particle production
- Analyzed non-analytic behavior in particle production rates

## Abstract

We discuss several aspects of particle production in: (a) time dependent electric field and (b) expanding Friedmann background. In the first part of the paper, we provide an algebraic mapping between the differential equations describing these two phenomena. This mapping allows a direct comparison between (a) and (b) and we highlight several interesting features of both cases using this approach. We determine the form of the (equivalent) electric field corresponding to different Friedmann spacetimes and discover, for example, a time-dependent electric field which, in a specific limit, leads to a Planck's spectrum of particles. We also discuss the conditions under which the particle production in an expanding background will be non-analytic in the parameter which encodes the coupling to the curved spacetime, in close analogy with the generalized Schwinger effect. In the second part of the paper, we study the situation in which both time dependent electric field and an expanding background are simultaneously present. We compute particle production rate in this context by several different methods paying special attention to its limiting forms and possible non-analytic behaviour. We also clarify several conceptual issues related to definitions of in-vacuum and out-vacuum in these systems.