Cosmological evolution of Witten superconducting string networks

We consider the evolution of current-carrying cosmic string networks described by the charge-velocity-dependent one scale (CVOS) model beyond the linear equation of state regime, specifically focusing on the Witten superconducting model. We find that, generically, for almost chiral currents, the network evolution reduces dynamically to that of the linear case, which has been discussed in our previous work. However, the Witten model introduces a maximum critical current which constrains the network scaling behaviour during the radiation era when currents can grow and approach this limit. Unlike the linear model, only if the energy density in the critical current is comparable to the bare string tension will there be substantial backreaction on the network evolution, thus changing the observational predictions of superconducting strings from those expected from a Nambu-Goto network. During the matter era, if there are no external sources, then dynamical effects dilute these network currents and they disappear at late times.