Cosmic Electromagnetic Fields due to Perturbations in the Gravitational Field

TL;DR

This paper investigates how primordial magnetic fields interact with density and gravitational wave perturbations in the early universe using gauge-invariant perturbation theory, analyzing their evolution across different conductivity regimes.

Contribution

It generalizes and corrects previous models by analyzing electromagnetic perturbations in various conductivity regimes within a non-linear gauge-invariant framework.

Findings

Electric field rotation dominates small-scale power spectrum

Modes cross the horizon during evolution

Numerical power spectra show mode behavior across regimes

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 Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. We compare the effects of this coupling under the assumptions of poor conductivity, infinite 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 rotation of the electric field dominates the power spectrum on small scales, in agreement with previous arguments.