Cosmic string formation by flux trapping

TL;DR

This paper investigates cosmic string formation through flux trapping in simulations, revealing how initial flux levels influence string network structure, infinite string persistence, and the transition akin to the Hagedorn transition.

Contribution

It introduces a numerical simulation approach to study flux trapping in cosmic string formation, highlighting effects of initial flux on network properties and transitions.

Findings

String networks resemble Kibble-Zurek mechanism at initial flux ~1

Higher initial flux increases infinite string length fraction

Strings in bundles do not stay together beyond correlation length

Abstract

We study the formation of cosmic strings by confining a stochastic magnetic field into flux tubes in a numerical simulation. We use overdamped evolution in a potential that is minimized when the flux through each face in the simulation lattice is a multiple of the fundamental flux quantum. When the typical number of flux quanta through a correlation-length-sized region is initially about 1, we find a string network similar to that generated by the Kibble-Zurek mechanism. With larger initial flux, the loop distribution and the Brownian shape of the infinite strings remain unchanged, but the fraction of length in infinite strings is increased. A 2D slice of the network exhibits bundles of strings pointing in the same direction, as in earlier 2D simulations. We find, however, that strings belonging to the same bundle do not stay together in 3D for much longer than the correlation length. As the initial flux per correlation length is decreased, there is a point at which infinite strings disappear, as in the Hagedorn transition.