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Spectator Composes a Gravitational Canon: Spectator-field-triggered Phase Transition During Inflation and its Anisotropic Gravitational Wave Signals

Yunjia Bao, Keisuke Harigaya

TL;DR

This work introduces a spectator-field mechanism to trigger a phase transition during inflation, producing topological defects whose horizon reentry yields gravitational waves with large-scale anisotropies. The timing of the transition is modulated by spectator fluctuations, imprinting spatial variation in the GW background and enabling observable anisotropies without requiring large inflaton excursions. The authors analyze two explicit realizations—cosmic strings and domain walls—providing analytic links between spectator fluctuations, reentry scales, and the anisotropic GW signal, and discuss observational constraints from LVK, Planck, and future GW observatories. The framework offers a versatile, SUSY-friendly path to anisotropic GWs with potential connections to MSSM Higgs dynamics and curvaton-like perturbations, broadening the space of cosmological probes of high-energy physics during inflation.

Abstract

We propose a general framework in which a phase transition is triggered during cosmic inflation by the slow-roll dynamics of a spectator field. The topological defects formed at the transition are inflated outside the horizon, reenter it after inflation, and can subsequently generate characteristic gravitational-wave (GW) signals. Quantum fluctuations of the spectator field modulate the timing of the transition, imprinting large-scale anisotropies in the resulting GW background. As an explicit realization, the spectator field may be identified with the Higgs field in a supersymmetric Standard Model. More generally, our framework applies to a wide class of spectator-modulated phenomena, providing a generic mechanism for producing anisotropic GW signals.

Spectator Composes a Gravitational Canon: Spectator-field-triggered Phase Transition During Inflation and its Anisotropic Gravitational Wave Signals

TL;DR

This work introduces a spectator-field mechanism to trigger a phase transition during inflation, producing topological defects whose horizon reentry yields gravitational waves with large-scale anisotropies. The timing of the transition is modulated by spectator fluctuations, imprinting spatial variation in the GW background and enabling observable anisotropies without requiring large inflaton excursions. The authors analyze two explicit realizations—cosmic strings and domain walls—providing analytic links between spectator fluctuations, reentry scales, and the anisotropic GW signal, and discuss observational constraints from LVK, Planck, and future GW observatories. The framework offers a versatile, SUSY-friendly path to anisotropic GWs with potential connections to MSSM Higgs dynamics and curvaton-like perturbations, broadening the space of cosmological probes of high-energy physics during inflation.

Abstract

We propose a general framework in which a phase transition is triggered during cosmic inflation by the slow-roll dynamics of a spectator field. The topological defects formed at the transition are inflated outside the horizon, reenter it after inflation, and can subsequently generate characteristic gravitational-wave (GW) signals. Quantum fluctuations of the spectator field modulate the timing of the transition, imprinting large-scale anisotropies in the resulting GW background. As an explicit realization, the spectator field may be identified with the Higgs field in a supersymmetric Standard Model. More generally, our framework applies to a wide class of spectator-modulated phenomena, providing a generic mechanism for producing anisotropic GW signals.
Paper Structure (13 sections, 52 equations, 3 figures)

This paper contains 13 sections, 52 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Light Spectator During Inflation
  3. Phase Transition During Inflation Triggered by Light Spectator
  4. Gravitational-Wave Anisotropy Signal
  5. GW Anisotropy from Cosmic Strings.
  6. GW Anisotropy from Domain Walls.
  7. Conclusion
  8. Cosmic Perturbations from Spectator-Modulated Phase Transition
  9. Cosmic Strings
  10. Domain Walls
  11. Symmetry Breaking by Two Fields
  12. Model Realization: GW Anistropy from Higgs-driven $B-L$ Strings
  13. Sensitivities for GW Anisotropy

Figures (3)

  • Figure 1: Schematic of the mechanism. Top Left (a): A fluctuation of the spectator field value $\sigma$ early in the inflation epoch imprints as a fluctuation in the phase transition (PT) timing during inflation. This changes when PT happens in different Hubble patches. Bottom (b): The fluctuation in PT timing at large distance $k^{-1}$ changes the horizon size $k_\text{re}^{-1}$ when the PT defects reenter. When the mode $k$ reenters the horizon, a large-scale anisotropic gravitational-wave (GW) signal appears if the GW spectrum $\Omega_\text{GW}$ depends on $k_\text{re}$. Top Right (c): GW spectrum is modulated because of the reentry timing. Here, we take GWs produced by cosmic strings as an example. Modulation in $k_\text{re}$ changes the UV rolloff scale. This modulation is at large scales because it comes from the early fluctuation of $\sigma$ during inflation.
  • Figure 2: Benchmark spectra for gravitational-wave (GW) anisotropy produced by spectator-modulated cosmic string reentry. While the string tension $\mu$ controls the plateau of the isotropic signal, the comoving reentry scale $k_\text{re}$ of the string alters the UV rolloff scale. A modulation in $k_\text{re}$ leads to an anisotropic signal $\Omega_\text{GW, aniso}(\ell,f)$ in higher multipoles on top of the isotropic background. Our Benchmark 1 is taken at $(\sqrt{\mu}, k_\text{re}/(2\pi), \beta, H_I/(2\pi \sigma_c)) = (3E14\GeV, E-3\Hz, 10^{-1}, 10^{-1})$, and Benchmark 2 is taken at $(\sqrt{\mu}, k_\text{re}/(2\pi), \beta, H_I/(2\pi \sigma_c)) = (3E14\GeV, 10\Hz, 10^{-2}, 10^{-2})$. The current exclusions from LIGO-Virgo-KAGRA's first part of the fourth observing run (LVK O4a) LIGOScientific:2025bkz, CMB measurement of $\Delta N_\text{eff}$Planck:2018vyg, and GW isocurvature perturbations Planck:2018jri (see Appendix \ref{['app:CurvePertStr']}), and the prospects of future searches (LISA LISACosmologyWorkingGroup:2022kbp, BBO Cui:2023dloSchmitz:2020syl, and ET Cui:2023dloMentasti:2020yydSchmitz:2020syl) of GW anisotropy are provided for comparison. Details of the GW constraints and prospects are provided in Appendix \ref{['app:GWSensitivity']}.
  • Figure 3: Schematic for the evolution of the field values in the two-field symmetry breaking discussed in App. \ref{['app:two fields']}. Initially, both charge-1 field $\chi_1$ and charge-2 field $\chi_2$ have no field values during inflation. When the spectator field $\sigma$ crosses a threshold, $\chi_1$ rolls to a minimum generated by the tachyonic Hubble-induced mass. $\chi_2$ field may obtain a tiny field value by coupling to $\chi_1$. After inflation, $\chi_1$'s Hubble-induced mass term becomes negligible while $\chi_2$'s tachyonic vacuum mass becomes significant and drives $\chi_2$ to a new field value. In the supersymmetric realization, $\chi_1$ can be identified with right-handed sneutrino $N$, $\chi_2$ with the $B-L$ breaking scalar, and $\sigma$ with the Higgs field as discussed in App. \ref{['app:SUSY']}.