Evolution of cosmic string configurations

TL;DR

This work develops a comprehensive analytic framework for the evolution of cosmic string networks by modeling the end-to-end distance distribution of left-moving string segments with a Gaussian Ansatz and three key length scales: $\xi$, $\bar{\xi}$, and $\zeta$. It derives coupled rate equations that couple stretching, intercommuting, loop formation, and gravitational radiation, and analyzes the conditions under which the scales exhibit horizon-scale scaling. The findings show that $\xi$ and $\bar{\xi}$ can scale with the horizon, while $\zeta$ grows only slowly and may later scale under strong gravitational back-reaction, implying a nuanced multi-scale scaling regime governed by parameters $k$ and $\hat{C}$. These results illuminate the role of small-scale structure and angular correlations in the long-term dynamics and have implications for gravitational-wave and CMB signatures from string networks.

Abstract

We extend and develop our previous work on the evolution of a network of cosmic strings. The new treatment is based on an analysis of the probability distribution of the end-to-end distance of a randomly chosen segment of left-moving string of given length. The description involves three distinct length scales: $ξ$, related to the overall string density, $\barξ$, the persistence length along the string, and $ζ$, describing the small-scale structure, which is an important feature of the numerical simulations that have been done of this problem. An evolution equation is derived describing how the distribution develops in time due to the combined effects of the universal expansion, of intercommuting and loop formation, and of gravitational radiation. With plausible assumptions about the unknown parameters in the model, we confirm the conclusions of our previous study, that if gravitational radiation and small-scale structure effects are neglected, the two dominant length scales both scale in proportion to the horizon size. When the extra effects are included, we find that while $ξ$ and $\barξ$ grow, $ζ$ initially does not. Eventually, however, it does appear to scale, at a much lower level, due to the effects of gravitational back-reaction.

Figures (6)

• Figure 1: Two contiguous segments
• Figure 2: Three contiguous segments
• Figure 3: Effect of intercommuting
• Figure 4: Position of excised loop segment
• Figure 5: Excision of a small loop