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

TL;DR

This paper formulates and analyzes an extended VOS framework for a three-type cosmic-string network (F-, D1-, D2- strings) arising from Spin(4N) Yang–Mills theory, focusing on how small reconnection probabilities shape scaling and gravitational-wave signatures. Analytically and numerically, it shows that the network can exhibit dramatically delayed scaling, which in turn suppresses the high-frequency GW spectrum while leaving low-frequency features intact. The results yield distinctive GW predictions, including potential compatibility with NANOGrav signals and clear high-frequency suppression patterns, and provide insights relevant to cosmic superstring scenarios with multi-tension spectra. The work highlights how multicomponent string interactions and tunable reconnection probabilities can imprint observable cosmological signals across current and future GW experiments.

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.

Figures (20)

• Figure 1: Schematic illustration of a zipper-type interaction.
• Figure 2: Schematic illustration of a straight section.
• Figure 3: Time evolution of $\gamma_1$ (left panel) and $\gamma_3$ (right panel) in the RD era for $P_1 = P_2 = 10^{-3}$ and $P_{\rm loop} = 10^{-6}$. We vary $P_3$ from $10^{-2}$ to $10^{-3}$, as indicated by different colors and line styles.
• Figure 4: Scaling values of $\gamma_1$ (left) and $\gamma_3$ (right) as functions of $P_3$ in the RD era, for $P_{\rm loop} = 10^{-6}$. We take $P_1 = P_2$ from $10^{0}$ to $10^{-8}$ (shown in different colors and line styles, from top to bottom in the right panel). In the left panel, all curves overlap and are indistinguishable.
• Figure 5: Same as Fig. \ref{['plot-final value']}, but as functions of $P_1 = P_2$ for $P_{\rm loop} = 10^{-4}$ in RD. We take $P_3$ from $10^{0}$ to $10^{-8}$ (from top to bottom in the left panel, and from bottom to top in the right panel).