Evolution of a Non-Abelian Cosmic String Network

Abstract

We describe a numerical simulation of the evolution of an $S_3$ cosmic string network which takes fully into account the non-commutative nature of the cosmic string fluxes and the topological obstructions which hinder strings from moving past each other or intercommuting. The influence of initial conditions, string tensions, and other parameters on the network's evolution is explored. Contrary to some previous suggestions, we find no strong evidence of the ``freezing'' required for a string-dominated cosmological scenario. Instead, the results in a broad range of regimes are consistent with the familiar scaling law; i.e., a constant number of strings per horizon volume. The size of this number, however, can vary quite a bit, as can other overall features. There is a surprisingly strong dependence on the statistical properties of the initial conditions. We also observe a rich variety of interesting new structures, such as light string webs stretched between heavier strings, which are not seen in Abelian networks.