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

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. 1 Introduction The study of cosmological magnetic fields has many motivations. Any primordial magnetic field could provide a seed field for dynamo amplification in disc galaxies, and fields of order 10 \Gamma10 gauss would create significant magnetic fields in galaxy clusters through adiabatic compression alone, [1]- [8]. It would also introduce new ingredients into the standard, but necessarily uncertain, picture of the very early universe. Large-..