Challenges for creating magnetic fields by cosmic defects

TL;DR

This paper investigates whether cosmic topological defects can generate magnetic fields via the Harrison mechanism during the radiation era, concluding that linear gravitational effects alone are insufficient for magnetic field production.

Contribution

It provides a detailed relativistic derivation of the Harrison mechanism at first order and demonstrates the necessity of anisotropic stress for vorticity and magnetic field generation.

Findings

Harrison mechanism is only efficient above T ~ 0.2 keV.

Vector metric perturbations cannot induce vorticity at linear order.

Anisotropic stress is required to generate vorticity and magnetic fields.

Abstract

We analyse the possibility that topological defects can act as a source of magnetic fields through the Harrison mechanism in the radiation era. We give a detailed relativistic derivation of the Harrison mechanism at first order in cosmological perturbations, and show that it is only efficient for temperatures above T ~ 0.2 keV. Our main result is that the vector metric perturbations generated by the defects cannot induce vorticity in the matter fluids at linear order, thereby excluding the production of currents and magnetic fields. We show that anisotropic stress in the matter fluids is required to source vorticity and magnetic fields. Our analysis is relevant for any mechanism whereby vorticity is meant to be transferred purely by gravitational interactions, and thus would also apply to dark matter or neutrinos.