Models for Small-Scale Structure on Cosmic Strings: II. Scaling and its stability

TL;DR

This paper extends a velocity-dependent one-scale model to analyze the evolution and stability of small-scale structures on cosmic strings, emphasizing the role of energy loss mechanisms and comparing results across cosmic eras.

Contribution

It introduces a simple ansatz for energy loss in the extended model and provides a systematic method to identify and analyze the stability of all possible scaling solutions.

Findings

Scaling is easier to achieve in the matter era than in the radiation era.

Stability constraints limit the range of energy loss parameters.

The model's predictions align with previous Goto-Nambu simulations.

Abstract

We make use of the formalism described in a previous paper [Martins {\it et al.} Phys. Rev. D90 (2014) 043518] to address general features of wiggly cosmic string evolution. In particular, we highlight the important role played by poorly understood energy loss mechanisms and propose a simple ansatz which tackles this problem in the context of an extended velocity-dependent one-scale model. We find a general procedure to determine all the scaling solutions admitted by a specific string model and study their stability, enabling a detailed comparison with future numerical simulations. A simpler comparison with previous Goto-Nambu simulations supports earlier evidence that scaling is easier to achieve in the matter era than in the radiation era. In addition, we also find that the requirement that a scaling regime be stable seems to notably constrain the allowed range of energy loss parameters.