Evolution of a global string network in a matter dominated universe

TL;DR

This study uses numerical simulations to analyze the evolution of global string networks in a matter-dominated universe, confirming the scaling solution and fitting the loop distribution with the one-scale model.

Contribution

It extends the understanding of global string network evolution to matter-dominated universes, confirming the scaling solution and loop distribution matches the one-scale model.

Findings

The scaling parameter $\xi$ is approximately 0.6 in matter domination.

The loop distribution function fits the one-scale model prediction.

Global string network evolution is well described by the one-scale model in matter domination.

Abstract

We evolve the network of global strings in the matter-dominated universe by means of numerical simulations. The existence of the scaling solution is confirmed as in the radiation-dominated universe but the scaling parameter $\xi$ takes a slightly smaller value, $\xi \simeq 0.6 \pm 0.1$, which is defined as $\xi = \rho_{s} t^{2} / \mu$ with $\rho_{s}$ the energy density of global strings and $\mu$ the string tension per unit length. The change of $\xi$ from the radiation to the matter-dominated universe is consistent with that obtained by Albrecht and Turok by use of the one-scale model. We also study the loop distribution function and find that it can be well fitted with that predicted by the one-scale model, where the number density $n_{l}(t)$ of the loop with the length $l$ is given by $n_{l}(t) = \nu/[t^2 (l + \kappa t)^2]$ with $\nu \sim 0.040$ and $\kappa \sim 0.48$. Thus, the evolution of the global string network in the matter-dominated universe can be well described by the one-scale model as in the radiation-dominated universe.