Metastable cosmic strings are broken at the start

TL;DR

This paper demonstrates that metastable cosmic strings typically break very early in the Universe, due to finite-temperature effects or inflationary monopoles, producing finite, often super-horizon segments and altering the expected gravitational-wave signatures. It develops analytic estimates and numerical results for the initial segment lengths, monopole abundances, and percolation, showing that early-time breaking can dominate over late-time quantum tunnelling for a wide range of κ≡m_M^2/μ. By incorporating nonuniform string tension through tension distributions extracted from simulations, it finds that high-tension regions can dominate decay rates, leading to earlier destruction than traditionally assumed. The analysis also connects these dynamics to the stochastic gravitational wave background, finding that larger κ values are often required to reproduce PTA-like signals, and discusses implications for hidden-sector flux tubes and dark QCD-like theories.

Abstract

We show that metastable cosmic strings break at early times, either via finite-temperature effects or by attaching to pre-existing monopoles during network percolation. The resulting segments can be initially super-horizon in size and thus persist for a significant amount of time. If the strings do not re-percolate, the network's eventual destruction is typically due to this early-time breaking rather than late-time quantum tunnelling. Survival of strings to epochs probed by NANOGrav requires $m_M^2/μ\gtrsim 10^3$, where $m_M$ and $μ$ are the monopole mass and the string tension respectively, over an order of magnitude larger than previous estimates. We also revisit quantum-tunnelling induced breaking. Results from numerical simulations suggest that this occurs mainly at rare high-tension points on the strings, yielding a rate much larger than is usually assumed. We briefly discuss the related scenario of flux tubes in a dark QCD-like hidden sector with dark-quark masses above the confinement scale.

Figures (9)

• Figure 1: Cartoon of the instanton solutions (white) on the Euclidean worldsheet (grey) with period $\beta = 1/T$, in different temperature regimes, relative to $T_0=\mu/(2m_M)$, which is the inverse size of the vacuum instanton.
• Figure 2: The typical distance between string endpoints, $\ell_0$, soon after network formation, in units of the Hubble length at that time $H_\star^{-1}$. The results are plotted as a function of $\kappa\equiv m_M^2/\mu$, where $m_M$ is the monopole mass and the string tension $\mu$ is fixed to satisfy $G_{\rm N}\mu = 10^{-7}$. The yellow line shows the endpoint separation if breaking occurred only at the zero-temperature rate ($T = 0$). The blue lines include finite-temperature effects, due to the enhanced breaking rate (Eq. \ref{['eq:l0finiteT']}) and pre-existing monopoles produced from the thermal bath (Eq. \ref{['eq:ell0']}). For the latter, we conservatively assume the correlation length $\xi \simeq T_\star^{-1}$ and $T_{\rm RH} \simeq v$. The red shaded region indicates values of $\kappa$ for which typical segments lie within a single Hubble patch and the network decays rapidly.
• Figure 3: Example of a string segment in our numerical simulations of string percolation, connecting a monopole (blue points) and an antimonopole (cyan points), circled red. The initial monopole number density is taken to be $n_M = 10^{-2} H_I^3$ and the random walk step size is $H_I^{-1}$.
• Figure 4: Left: Binned distribution of lengths of string segments for a monopole number density $n_M = 10^{-3} \xi^{-3}$ where $\xi$ is the correlation length, extracted from $10^4$ random walk simulations. The expected distribution, $P(\ell)= (\ell /\ell_i^2)\,e^{-\ell/\ell_i}$ with $\ell_i=\xi^{-2}/n_M$ (see Eq. \ref{['eq:segmentdistribution']}), is shown in blue; the expected average $\ell_i$ approximately coincides with the true average (red dashed line). Right: The same but for string loops. The blue line is now a best-fit distribution of the form $P(\ell)=b\ell \, e^{-a \ell/\xi} + d \,e^{-c\ell/\xi}$, with numerical values $a=0.112$, $b=8.25\cdot10^{-3} \xi^{-2}$, $c = 6.93\cdot10^{-3}$ and $d = 2.15\cdot10^{-3} \xi^{-1}$. At the value of the monopole density shown, around $28\%$ of strings form loops, which are typically much shorter than the segments.
• Figure 5: Left: Distribution of tensions for an Abelian-Higgs critical string network (with straight string tension $\mu_0 = 2\pi v^2$) extracted from numerical simulations, with statistical uncertainties (shaded). The red lines show the best-fit behaviour in the regions $\mu < 1.7\mu_0$ and $\mu > 1.7\mu_0$ respectively. Right: The number of breaking events per Hubble time and Hubble length due to string regions with tension between $\mu$ and $\mu+d\mu$ at different cosmological times in radiation domination, based on the fit of Eq. \ref{['eq:latetimeFit']} extrapolated to $\mu/\mu_0 \simeq 3$. Breaking dominantly happens at rare high-tension regions, since the enhancement of the breaking from the increased tension outweighs the rarity of such regions. We fix $\kappa = 144$, and plot the results at different values of Hubble (labelled by cosmic temperature) and for two values of tension, $G_{\rm N}\mu_0 = 10^{-7}$ (thick lines) and $G_{\rm N}\mu_0 = 10^{-10}$ (dashed lines).

Theorems & Definitions (2)

• Claim
• proof