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Searching Stochastic Gravitational Wave Background Landscape Across Frequency Bands

Yunjia Bao, Tore Boybeyi, Vuk Mandic, Lian-Tao Wang

TL;DR

This work develops a unified Bayesian framework to map the stochastic gravitational-wave background across frequency bands, using a concrete new-physics model in which a two-step phase transition separated by inflation yields domain walls bounded by either gauge or global cosmic strings. The GW signal comprises a wall component and a string component, with distinct dependence on the three core parameters $H_{ m re}$, $v_2$, and $oldsymbol{}$, and it predicts characteristic UV knees and peak features that imprint across PTA, LVK, and future space-based detectors. Current data from NANOGrav and LVK constrain parts of the parameter space (e.g., $ ext{v}_2 \, aisebox{0.5pt}{ extendash}\, 10^{15} ext{ GeV}$ for the string component; $ riangle N_{ m eff}$ bounds remain powerful at high frequencies), while Bayesian model comparison indicates the hybrid string-wall scenario can modestly improve fits to the NANOGrav data relative to SMBHB-only interpretations when a SMBHB foreground is included. The study highlights the power of multi-band observations: LISA and CE are expected to decisively test the Scenario 1 gauge-string realization by probing its UV tail, and a joint LISA-CE detection would enable precise determination of all three model parameters, thereby mapping early-universe dynamics and testing the existence of hybrid topological defects.

Abstract

Gravitational wave (GW) astrophysics is entering a multi-band era with upcoming GW detectors, enabling detailed mapping of the stochastic GW background across vast frequencies. We highlight this potential via a new physics scenario: hybrid topological defects from a two-step phase transition separated by inflation. We develop a general pipeline to analyze experimental exclusions and apply it to this model. The model offers a possible explanation of the pulsar timing array signal at low frequencies, and future experiments (LISA/Cosmic Explorer/Einstein Telescope) will confirm or rule it out via the higher-frequency probes, showcasing the power of multi-band constraints.

Searching Stochastic Gravitational Wave Background Landscape Across Frequency Bands

TL;DR

This work develops a unified Bayesian framework to map the stochastic gravitational-wave background across frequency bands, using a concrete new-physics model in which a two-step phase transition separated by inflation yields domain walls bounded by either gauge or global cosmic strings. The GW signal comprises a wall component and a string component, with distinct dependence on the three core parameters , , and , and it predicts characteristic UV knees and peak features that imprint across PTA, LVK, and future space-based detectors. Current data from NANOGrav and LVK constrain parts of the parameter space (e.g., for the string component; bounds remain powerful at high frequencies), while Bayesian model comparison indicates the hybrid string-wall scenario can modestly improve fits to the NANOGrav data relative to SMBHB-only interpretations when a SMBHB foreground is included. The study highlights the power of multi-band observations: LISA and CE are expected to decisively test the Scenario 1 gauge-string realization by probing its UV tail, and a joint LISA-CE detection would enable precise determination of all three model parameters, thereby mapping early-universe dynamics and testing the existence of hybrid topological defects.

Abstract

Gravitational wave (GW) astrophysics is entering a multi-band era with upcoming GW detectors, enabling detailed mapping of the stochastic GW background across vast frequencies. We highlight this potential via a new physics scenario: hybrid topological defects from a two-step phase transition separated by inflation. We develop a general pipeline to analyze experimental exclusions and apply it to this model. The model offers a possible explanation of the pulsar timing array signal at low frequencies, and future experiments (LISA/Cosmic Explorer/Einstein Telescope) will confirm or rule it out via the higher-frequency probes, showcasing the power of multi-band constraints.

Paper Structure

This paper contains 14 sections, 52 equations, 13 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical Models
  3. New Physics Scenario 1: Walls Bounded by Gauge Cosmic Strings
  4. New Physics Scenario 2: Walls Bounded by Global Cosmic Strings
  5. Methodology
  6. Results
  7. Conclusion and Discussion
  8. Construction of SGWB Sensitivities
  9. Noise Power Spectral Densities
  10. GW Spectrum of Cosmic String Network
  11. GW Spectrum of Gauge Strings
  12. GW Spectrum of Global Strings
  13. Astrophysical Foreground: Supermassive Black Hole Binaries in nHz
  14. Full Triangle Plots and Other Best-fit Figures

Figures (13)

  • Figure S1: $\Omega_N$ and $\Omega_{\rm PLIS}$ for LISA and CE for $T=3$ yrs and $\varrho_{\text{thr}}=2$.
  • Figure S2: Exemplary spectrum for Gauge Walls and Strings with $H_{\rm re} = 10^{-10}\rm \ GeV$.
  • Figure S3: Exemplary spectrum for Global Walls and Strings. Left:$H_{\rm re}=10^{-15} \rm \ GeV$, $\sigma=10^{18} \rm \ GeV^3$. Right:$H_{\rm re}=10^{18} \rm \ GeV$.
  • Figure S4: New Physics Scenario 1. Full triangle (corner) plot for the “(Gauge) Wall + String” model, with (blue) and without (red) an SMBHB foreground. Shaded contours mark the 68% and 95% credible regions; diagonal panels show the 1D marginals for $(\log_{10}H_{\rm re},\,\log_{10}\sigma,\,\log_{10}v_2)$ and, when present, the SMBHB parameters $(\log_{10}A_{\rm BHB},\,\gamma_{\rm BHB})$.
  • Figure S5: New Physics Scenario 2. Same as (a) but for the “(Global) Wall + String” model, comparing fits with (blue) and without (red) an SMBHB foreground.
  • ...and 8 more figures