Multifaceted Supercooling: From PTA to LIGO

TL;DR

The paper investigates how a strongly supercooled first-order phase transition (scFOPT) that triggers a brief thermal inflation reshapes gravitational waves from a pre-existing metastable cosmic-string network. It shows vacuum-energy domination suppresses high-frequency GW emission by freezing the string network and delaying horizon re-entry, thereby reopening PTA-favored parameter space while remaining compatible with LIGO constraints; it also predicts an additional GW component from the phase transition, yielding a distinctive multi-source spectrum with a spectral break $f_{ m brk}^{\rm sc}$. The authors develop a numerical, multifaceted analysis using the VOS framework with six coupled ODEs to track the radiation and vacuum components, network length, and velocities, and they classify viable regions into three categories relative to detector sensitivities. They also discuss the potential for SIGWs and PBH DM in these scenarios and outline observational prospects for LVK-D, LISA, DECIGO, and ET, highlighting the importance of multi-band GW data and Bayesian inference to distinguish this history from alternative cosmologies.

Abstract

Supercooled phase transitions, as predicted, e.g., in near-conformal and confining extensions of the Standard Model (SM), are established sources of strong stochastic gravitational wave backgrounds (SGWBs). In this work, we investigate another facet of such transitions: their significant and largely uncharted impact on gravitational wave spectra originating from independent cosmological sources. Focusing on gravitational waves produced by a metastable cosmic string network, we show that an intervening supercooled phase, initiating thermal inflation, can reshape and suppress the high-frequency part of the spectrum. This mechanism reopens regions of string parameter space previously excluded by LIGO's null results, while remaining compatible with the nanohertz SGWB signal reported by pulsar timing arrays (PTAs). The resulting total spectrum typically exhibits a dual-component structure, sourced by both string decay and the phase transition itself, rendering the scenario observationally distinctive. We systematically classify the viable parameter space and identify regions accessible to upcoming detectors such as Advanced LIGO, LISA, and ET.

Figures (11)

• Figure 1: After formation, the string network enters a scaling regime with $L \sim a^2$, where $L$ is the long-string correlation length and $a$ is the scale factor. During supercooling, the rapid expansion stretches the network beyond the horizon, halting loop production, and the correlation length scales as $L \sim a$. After supercooling, as the universe reheats, the strings gradually re-enter the horizon and the network returns to scaling with $L \sim a^2$. This figure is generated using Eqs. \ref{['rad']}--\ref{['avsz']}, with the scale factor normalized to unity at $z = z_{\rm in}$. We maintain this normalization in all subsequent figures where $a$ is shown.
• Figure 2: Top Left: Evolution of $\xi$ and $\tilde{v}$. Top Right: Evolution of the long string correlation length normalized to the Hubble horizon. Bottom Left: Evolution of the loop production efficiency $A_\beta$ for different numbers of e-folds during the supercooled phase. Bottom Right: Evolution of $\xi$ and $\tilde{v}$ as functions of the scale factor $a$.
• Figure 3: Left: Gravitational wave spectra for $G\mu = 10^{-7}$, $\sqrt{\kappa} = 7.9$, and $T_{\rm RH} = 10^7~\mathrm{GeV}$, shown for different values of the number of e-folds $N_e$. Right: Gravitational wave spectra for $G\mu = 10^{-7}$, $\sqrt{\kappa} = 7.9$, and fixed $N_e = 10$, plotted for varying reheating temperatures $T_{\rm RH}$. In both panels, the dashed vertical lines indicate the fitted spectral break corresponding to the analytically derived reheating temperature $T_{\rm re}$.
• Figure 4: Left: Colored regions on the $G\mu$–$\sqrt{\kappa}$ plane, labeled by different values of $T_{\rm RH}$, correspond to gravitational wave spectra with plateau amplitudes $\Omega_{\rm GW}^{\rm plt,\infty} \gtrsim \Omega_{\rm GW}^{\rm LIGO-O3} \equiv 1.7 \times 10^{-8}$ and are therefore testable with LVK-Design sensitivity at $25~\mathrm{Hz}$. In the absence of supercooling, these regions would be excluded by LIGO-O3, since the spectra do not fall off sufficiently at $f \ll 25~\mathrm{Hz}$ and exceed the observational bound. Gray contours indicate regions consistent with the NANOGrav 15-year data. Middle: Colored regions where $\Omega_{\rm GW}^{\rm LIGO-O3} \gtrsim \Omega_{\rm GW}^{\rm plt,\infty} \gtrsim \Omega_{\rm GW}^{\rm LVK-D} \equiv 2 \times 10^{-9}$. Although in principle testable by LVK-D, these parameter regions are already disfavored by PTA observations even without invoking supercooling, and thus are less relevant to our discussion. Right: Regions yielding lower GW amplitudes at LIGO frequencies, and therefore not accessible to LVK-D, but within reach of future detectors such as the ET. Benchmark points selected from each category are illustrated in the gravitational wave spectra shown in Fig. \ref{['fig5']} (left).
• Figure 5: Left: Representative GW spectra corresponding to the benchmark points selected from each category shown in Fig. \ref{['fig4']}. Right: Sensitivity of current and future GW detectors to the spectral break frequency. The NANOGrav 15-year confidence regions are indicated by the horizontal solid and dashed lines. The benchmark points from the left panel are also marked for reference.