Schwinger Effect in 4D de Sitter Space and Constraints on Magnetogenesis in the Early Universe

TL;DR

This paper analyzes the Schwinger effect in 4D de Sitter space, revealing how electric fields influence pair creation and conductivity, and constrains early universe magnetogenesis by showing electric fields can suppress large-scale magnetic field generation.

Contribution

It provides a detailed calculation of the induced current in de Sitter space and applies these results to place limits on primordial magnetic fields during inflation.

Findings

Weak electric fields lead to high conductivity in de Sitter space.

Generated magnetic fields during inflation are limited to below 10^{-30} G on Mpc scales.

Electric fields can terminate magnetogenesis by inducing large conductivity.

Abstract

We investigate pair creation by an electric field in four-dimensional de Sitter space. The expectation value of the induced current is computed, using the method of adiabatic regularization. Under strong electric fields the behavior of the current is similar to that in flat space, while under weak electric fields the current becomes inversely proportional to the mass squared of the charged field. Thus we find that the de Sitter space obtains a large conductivity under weak electric fields in the presence of a charged field with a tiny mass. We then apply the results to constrain electromagnetic fields in the early universe. In particular, we study cosmological scenarios for generating large-scale magnetic fields during the inflationary era. Electric fields generated along with the magnetic fields can induce sufficiently large conductivity to terminate the phase of magnetogenesis. For inflationary magnetogenesis models with a modified Maxwell kinetic term, the generated magnetic fields cannot exceed 10^{-30} G on Mpc scales in the present epoch, when a charged field carrying an elementary charge with mass of order the Hubble scale or smaller exists in the Lagrangian. Similar constraints from the Schwinger effect apply for other magnetogenesis mechanisms.