Evolution of a global string network in a matter dominated universe

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 $\xi ={\rho }_s{t}^2\mathrm{/}\mu$ 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.