Primordial magnetic fields from the string network

TL;DR

This paper investigates how cosmic string networks can generate primordial magnetic fields through vector mode perturbations, providing detailed spectrum calculations and suggesting these fields could seed larger cosmic magnetic fields.

Contribution

It introduces a detailed calculation of magnetic field generation from cosmic string networks using the one scale model, highlighting their potential role as seeds for cosmic magnetism.

Findings

Magnetic fields generated have a spectrum with specific power-law behaviors on different scales.

The magnetic field amplitude can reach around 10^{-17} to 10^{-18} Gauss at Mpc scales today.

Generated magnetic fields could serve as seeds for larger-scale cosmic magnetic fields.

Abstract

Cosmic strings are a type of cosmic defect formed by a symmetry-breaking phase transition in the early universe. Individual strings would have gathered to build a network, and their dynamical motion would induce scalar--, vector-- and tensor--type perturbations. In this paper, we focus on the vector mode perturbations arising from the string network based on the one scale model and calculate the time evolution and the power spectrum of the associated magnetic fields. We show that the relative velocity between photon and baryon fluids induced by the string network can generate magnetic fields over a wide range of scales based on standard cosmology. We obtain the magnetic field spectrum before recombination as $a^2B(k,z)\sim4\times10^{-16}G\mu/((1+z)/1000)^{4.25}(k/{\rm Mpc}^{-1})^{3.5}$ Gauss on super-horizon scales, and $a^2B(k,z)\sim2.4\times10^{-17}G\mu/((1+z)/1000)^{3.5}(k/{\rm Mpc}^{-1})^{2.5}$ Gauss on sub-horizon scales in co-moving coordinates. This magnetic field grows up to the end of recombination, and has a final amplitude of approximately $B\sim10^{-17\sim -18} G\mu$ Gauss at the $k\sim1\ {\rm Mpc}^{-1}$ scale today. This field might serve as a seed for cosmological magnetic fields.