Interactions of cosmological gravitational waves and magnetic fields

TL;DR

This paper investigates the mutual interactions between cosmological gravitational waves and magnetic fields, focusing on back-reaction effects and clarifying previous claims about their amplification and generation.

Contribution

It provides a second-order analysis of the back-reaction between gravitational waves and magnetic fields, clarifying the strength of their interactions and revisiting earlier claims.

Findings

Back-reaction effects are analyzed at second order.

Previous claims of strong amplification are revisited.

The role of gravitational waves in magnetic field evolution is clarified.

Abstract

The energy momentum tensor of a magnetic field always contains a spin-2 component in its anisotropic stress and therefore generates gravitational waves. It has been argued in the literature (Caprini & Durrer \cite{CD}) that this gravitational wave production can be very strong and that back-reaction cannot be neglected. On the other hand, a gravitational wave background does affect the evolution of magnetic fields. It has also been argued (Tsagas et al. \cite{Tsagas:2001ak},\cite{Tsagas:2005ki}) that this can lead to very strong amplification of a primordial magnetic field. In this paper we revisit these claims and study back reaction to second order.