Delayed Scaling of Multi-Type Cosmic F- and D-strings in VOS Models

TL;DR

This paper models the delayed scaling behavior of multi-type cosmic F- and D-strings using the VOS framework, revealing how reconnection probabilities influence the timing of reaching scaling and potential gravitational wave signatures.

Contribution

It extends the VOS model to multi-type strings, analytically and numerically analyzing their scaling behavior and implications for gravitational wave signals.

Findings

Scaling time can be extremely large for certain reconnection probabilities

Delayed scaling suppresses high-frequency gravitational wave signals

Analytical and numerical results are consistent

Abstract

We investigate the velocity-dependent one-scale (VOS) model to the case of one cosmic F-string and two D-strings as color flux tubes in pure Spin($4N$) gauge theory. We analytically calculate the scaling string density as a function of the reconnection probabilities, and confirm our results with numerical calculations. We also determine the timescale at which the string density reaches the scaling regime, and find that for certain values of the reconnection probability, the scaling time can become extremely large, by many orders of magnitude. This leads to a characteristic suppression signature of the gravitational-wave signal at high frequencies, which may become observable in the frequency range of future interferometric gravitational-wave observations.