Scaling solutions for current-carrying cosmic string networks. II. Biased solutions

The charge-velocity-dependent one-scale model is an extension of the canonical velocity-dependent one-scale model that explicitly incorporates additional degrees of freedom on the string world sheet, such as arbitrary currents and charges, expected in physically realistic models. A previous paper [] started an in-depth classification of its possible asymptotic scaling solutions, with the goal of identifying distinguishing features which may be tested against numerical simulations or future observations. This earlier analysis restricted itself to unbiased solutions; in the present work we relax this assumption, allowing for the possibility of energy loss biases between the bare string and the charge/current or between the charge and the current themselves. We find additional scaling solutions, some of which are parametric extensions of the unbiased ones, while others are new scaling branches that do not exist in the unbiased case. Overall, it remains the case that there are three broad classes of solutions, mainly depending on the balance between the expansion rate and the available energy loss mechanisms. Our results enable a quantitative calibration of the model, using forthcoming high-resolution numerical simulations.