Scaling Solutions of Wiggly Cosmic Strings

TL;DR

This paper analyzes the asymptotic scaling solutions of wiggly cosmic string networks, revealing three regimes of wiggliness and highlighting the influence of universe expansion and energy transfer mechanisms on network behavior.

Contribution

It provides a systematic study of the scaling solutions of the wiggly VOS model, clarifying the roles of different physical mechanisms in cosmic string network evolution.

Findings

Identified three distinct scaling regimes for wiggliness.

Full network scaling is more probable during the matter era.

Compared theoretical solutions with numerical simulation results.

Abstract

Cosmic string networks form during cosmological phase transitions as a consequence of the Kibble mechanism. The evolution of the simplest networks is accurately described by the canonical Velocity Dependent One-Scale (VOS) model. However, numerical simulations have demonstrated the existence of significant quantities of short-wavelength propagation modes on the strings, known as wiggles, which motivated the recent development of a wiggly string extension of the VOS. Here we summarize recent progress in the physical interpretation of this model through a systematic study of the allowed asymptotic scaling solutions of the model. The modeling mainly relies on three mechanisms: the universe's expansion rate, energy transfer mechanisms (e.g., the production of loops and wiggles), and the choice of the scale in which wiggles are coarse-grained. We consider the various limits in which each mechanism dominates and compare the scaling solutions for each case, in order to gain insight into the role of each mechanism in the overall behavior of the network. Our results show that there are three scaling regimes for the wiggliness, consisting of the well-known Nambu-Goto solution, and non-trivial regimes where the amount of wiggliness can grow as the network evolves or, for specific expansion rates, become a constant. We also demonstrate that full scaling of the network is more likely in the matter era than in the radiation epoch, in agreement with numerical simulations.