Generalised velocity-dependent one-scale model for current-carrying strings

Abstract

We develop an analytic model to quantitatively describe the evolution of superconducting cosmic string networks. Specifically, we extend the velocity-dependent one-scale (VOS) model to incorporate arbitrary currents and charges on cosmic string worldsheets under two main assumptions, the validity of which we also discuss. We derive equations that describe the string network evolution in terms of four macroscopic parameters: the mean string separation (or alternatively the string correlation length) and the root mean square (RMS) velocity which are the cornerstones of the VOS model, together with parameters describing the averaged timelike and spacelike current contributions. We show that our extended description reproduces the particular cases of wiggly and chiral cosmic strings, previously studied in the literature. This VOS model enables investigation of the evolution and possible observational signatures of superconducting cosmic string networks for more general equations of state, and these opportunities will be exploited in a companion paper.

Gravitational Waves from Global Cosmic Strings and Cosmic Archaeology

“…Recent years have seen rapid developments in simulating a global/axion string network [42][43][44][65][66][67][68][69][70][71]. Nevertheless, a technical challenge persists for pure numerical simulation to track the network's evolution over the entire relevant cosmic history.…”

Scaling solutions of wiggly cosmic strings

“…In other words, should pieces of string that have larger mass currents be given more weight in the average? Given the discussion so far, the first definition is more natural (and it is the one adopted in what follows), although the alternative choice deserves further discussion-see [24] for an alternative approach. These two different averaging procedures can be applied to any other relevant quantity.…”

“…Then [23] studied the particular case where the wiggliness was assumed to reach scaling, and also made a brief comparison with the simulations of [6]. The necessary formalism has been recently extended to the case of generic current-carrying cosmic strings [24].…”

Gravitational Waves from Current-Carrying Cosmic Strings

“…In order to obtain more realistic predictions, it is therefore necessary to go beyond this minimal description and consider, e.g., extensions of the simplest Nambu-Goto model featuring additional worldsheet degrees of freedom. Such degrees of freedom can be currents induced by charge carriers that propagate along cosmic strings [46,47], or, e.g., short-wavelength propagation modes known as wiggles [48]. In this paper, we will focus on the former possibility and consider neutral currents, i.e., currents of particles that are only charged under the Abelian gauge group whose spontaneous breaking results in the formation of the string network but that do not interact with any other gauge force.…”

“…Recently, the authors of Ref. [47] generalized the standard VOS model in order to account for the time evolution of this current. In our analysis, we will make use of these results and solve the generalized VOS equations derived in Ref.…”