Cosmic electromagnetic fields due to perturbations in the gravitational field

Abstract

We use non-linear gauge-invariant perturbation theory to study the interaction of an inflation produced seed magnetic field with density and gravitational wave perturbations in an almost FriedmannLemaître-Robertson-Walker (FLRW) spacetime with zero spatial curvature. We compare the effects of this coupling under the assumptions of poor conductivity, perfect conductivity and the case where the electric field is sourced via the coupling of velocity perturbations to the seed field in the ideal magnetohydrodynamic (MHD) regime, thus generalizing, improving on and correcting previous results. We solve our equations for long wavelength limits and numerically integrate the resulting equations to generate power spectra for the electromagnetic field variables, showing where the modes cross the horizon. We find that the interaction can seed Electric fields with non-zero curl and that the curl of the electric field dominates the power spectrum on small scales, in agreement with previous arguments.

On the Interaction Between Electromagnetic, Gravitational, and Plasma Related Perturbations on LRS Class II Spacetimes

“…Examples include mechanisms based on gravitational wave interactions [2][3][4], and velocity perturbations in the cosmological plasma [4]. Although some of the mechanisms for amplifying the seed fields have been suggested to be too weak [5][6][7], the prospect of a mechanism based on the dynamics of a self-gravitating plasma and classical general relativity is still enticing, since it would not explicitly depend on any additional exotic physics. Therefore, it is still of great interest to study the interactions between a cosmological plasma and general relativistic effects.…”

“…The studies of self-gravitating plasmas in a cosmological scenario seem to have mainly used a perturbative approach with the FLRW spacetimes as zeroth order backgrounds [2][3][4][5][6][7][8]. However, due to the isotropy of the FLRW spacetimes, it is essentially impossible to have a non-zero magnetic field 3-vector on the background, since that field would otherwise define a preferred spatial direction.…”

Post inflationary evolution of inflation-produced, large-scale magnetic fields using a generalised cosmological Ohm's law and both standard and modified Maxwell's equations

“…In this paper we examine cosmological magnetic fields generated during inflation. It is noteworthy that gravitational waves are also generated during inflation [8] as a counterpart. The energy transfer between the two is of interest and has been studied in [9].…”

Dynamo Theory, Nonlinear Magnetic Fields, and the Euler Potentials

“…It is thought that original magnetic fields, or seed fields as they are commonly called, may have their origin in phase transition in the early universe [2,3], or in the cosmological structure formation [4], or in the first stars and black holes [5], or in the first supernova [6], or even as a result of fluctuations in the gravitational field [7]. The authors of [8] gave an argument that places severe constraints on magneto-genesis theories of the early universe.…”