Scaling solutions for current-carrying cosmic string networks

Cosmic string networks are the best motivated relics of cosmological phase transitions, being unavoidable in many physically plausible extensions of the Standard Model. Most studies, including those providing constraints from and forecasts of their observational signals, rely on assumptions of featureless networks, neglecting the additional degrees of freedom on the string worldsheet, e.g. charges and currents, which are all but unavoidable in physically realistic models. An extension of the canonical velocity-dependent one-scale model, accounting for all such possible degrees of freedom, has been recently developed. Here we improve its physical interpretation by studying and classifying its possible asymptotic scaling solutions, and in particular how they are affected by the expansion of the Universe and the available energy loss or transfer mechanisms. We find three classes of solutions. For sufficiently fast expansion rates the charges and currents decay and one asymptotes to the Nambu-Goto case, while for slower expansion rates they can dominate the network dynamics. In between the two there is a third regime in which the network, including its charge and current, reaches full scaling. Under specific but plausible assumptions, this intermediate regime corresponds to the matter-dominated era. Our results agree with, and significantly extend, those of previous studies.