Magnetic fields in the early universe

TL;DR

This paper provides a pedagogical overview of magnetic fields in the early universe, focusing on electrodynamics in curved spacetime, magnetohydrodynamics in an expanding universe, and magnetic field generation during inflation.

Contribution

It introduces a detailed formulation of electrodynamics in curved spacetime and reviews models of magnetic field generation during inflation, highlighting potential issues like back reaction effects.

Findings

Derived magnetic and electric spectra for inflationary models

Discussed the role of tetrads in magnetohydrodynamics

Identified challenges in magnetic field generation during inflation

Abstract

We give a pedagogical introduction to two aspects of magnetic fields in the early universe. We first focus on how to formulate electrodynamics in curved space time, defining appropriate magnetic and electric fields and writing Maxwell equations in terms of these fields. We then specialize to the case of magnetohydrodynamics in the expanding universe. We emphasize the usefulness of tetrads in this context. We then review the generation of magnetic fields during the inflationary era, deriving in detail the predicted magnetic and electric spectra for some models. We discuss potential problems arising from back reaction effects and from the large variation of the coupling constants required for such field generation.