Charge-velocity-dependent one-scale linear model

TL;DR

This paper models the evolution of current-carrying cosmic string networks, showing how their scaling behavior depends on universe expansion, initial currents, and energy loss, with implications for early universe phenomenology.

Contribution

It introduces a linear equation of state formalism to analyze current-carrying string networks, revealing conditions for stable non-trivial currents and their dependence on cosmological parameters.

Findings

Fast expansion dilutes currents, leading to Nambu-Goto scaling.

Large initial currents can grow during radiation era with damping.

Current-carrying networks may exist in radiation era, affecting cosmological signals.

Abstract

We apply a recently developed formalism to study the evolution of a current-carrying string network under the simple but generic assumption of a linear equation of state. We demonstrate that the existence of a scaling solution with non-trivial current depends on the expansion rate of the universe, the initial root mean square current on the string, and the available energy loss mechanisms. We find that the fast expansion rate after radiation-matter equality will tend to rapidly dilute any pre-existing current and the network will evolve towards the standard Nambu-Goto scaling solution (provided there are no external current-generating mechanisms). During the radiation era, current growth is possible provided the initial conditions for the network generate a relatively large current and/or there is significant early string damping. The network can then achieve scaling with a stable non-trivial current, assuming large currents will be regulated by some leakage mechanism. The potential existence of current-carrying string networks in the radiation era, unlike the standard Nambu-Goto networks expected in the matter era, could have interesting phenomenological consequences.