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

Abstract: The charge-velocity-dependent one-scale model is an extension of the canonical velocity-dependent one-scale model which explicitly incorporates additional degrees of freedom on the string worldsheet, such as arbitrary currents and charges, expected in physically realistic models. A previous paper [Pimenta and Martins, Phys. Rev. D 110, 023540 (2024)] 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 one 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 which 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.