Evolution of Cosmic Necklaces and Lattices

Previously developed analytic models for the evolution of cosmic string and monopole networks are applied to networks of monopoles attached to two or more strings; the former case is usually known as cosmic necklaces. These networks are a common consequence of models with extra dimensions such as brane inflation. Our quantitative analysis agrees with (and extends) previous simpler estimates, but we will also highlight some differences. A linear scaling solution is usually the attractor solution for both the radiation and matter-dominated epochs, but other scaling laws can also exist, depending on the universe's expansion rate and the network's energy loss mechanisms.