A Gauge-invariant Analysis of Magnetic Fields in General Relativistic Cosmology

TL;DR

This paper develops a gauge-invariant, fully relativistic framework for analyzing large-scale primordial magnetic fields in cosmology, deriving exact non-linear equations and exploring their effects on universe perturbations and inflation.

Contribution

It introduces a comprehensive, gauge-invariant relativistic approach to cosmological magnetic fields, extending previous Newtonian models and including non-linear magnetohydrodynamic equations.

Findings

Small perturbations in Friedmann universes are characterized.

Relativistic results are compared with Newtonian treatments.

Effects of inflationary expansion on magnetic fields are examined.

Abstract

We provide a fully general-relativistic treatment of cosmological perturbations in a universe permeated by a large-scale primordial magnetic field, using the Ellis-Bruni gauge-invariant formalism. The exact non-linear equations for general relativistic magnetohydrodynamic evolution are derived. A number of applications are made: the behaviour of small perturbations to Friedmann universes are studied; a comparison is made with earlier Newtonian treatments of cosmological perturbations and some effects of inflationary expansion are examined.