Evolution of a global string network in a matter dominated universe

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 $ξ$ takes a slightly smaller value, $ξ\simeq 0.6 \pm 0.1$, which is defined as $ξ= ρ_{s} t^{2} / μ$ with $ρ_{s}$ the energy density of global strings and $μ$ the string tension per unit length. The change of $ξ$ 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 $n_{l}(t) = ν/[t^2 (l + κt)^2]$ with $ν\sim 0.040$ and $κ\sim 0.48$. 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.