Baryogenesis and Gravitational Wave Production

• Baryogenesis is the process generating the matter-antimatter imbalance through mechanisms like electroweak, Affleck–Dine, and PBH-induced scenarios in out-of-equilibrium conditions.
• Stochastic gravitational waves emanate from early-universe events such as first-order phase transitions, oscillon formation, and cosmic string decay, offering detectable signatures of these dynamics.
• Hydrodynamic modeling and lattice simulations reveal that bubble wall dynamics decouple the effective CP diffusion rate from the overall wall velocity, linking baryogenesis efficiency to GW signal strength.

Baryogenesis and Stochastic Gravitational Wave Production constitute a broad field connecting the microphysics of matter–antimatter asymmetry generation in the early universe with the stochastic gravitational wave backgrounds produced by out-of-equilibrium processes, most notably first-order phase transitions, nonperturbative scalar or fermion dynamics, and topological defect formation. The research focuses on the interplay between the mechanisms responsible for baryon number generation—such as electroweak baryogenesis, Affleck-Dine baryogenesis, or scenarios involving primordial black hole evaporation—and the generation of a detectable stochastic gravitational wave (GW) background sourced by the violent dynamics inherent to these processes.

1. Hydrodynamics of Bubble Expansion and Parameter Decoupling

During a first-order cosmological phase transition (such as an electroweak phase transition), bubbles of the low-temperature (broken) phase nucleate and expand in the hot plasma of the early universe. The expansion of these bubbles and their interaction with the plasma are governed by hydrodynamical matching conditions derived from local energy–momentum conservation. In the plasma rest frame, the energy–momentum tensor is expressed as:

$$T_{\mu\nu}^{\text{plasma}} = w\, u_\mu u_\nu - g_{\mu\nu} p$$

where $w$ is the enthalpy, $p$ the pressure, and $u_\mu$ the four-velocity.

The junction (Rankine-Hugoniot) conditions across the bubble wall, specifically

$$w_+ v_+^2 \gamma_+^2 + p_+ = w_- v_-^2 \gamma_-^2 + p_-$$

$w_+ v_+ \gamma_+^2 = w_- v_- \gamma_-^2$

(where $+$ and $-$ denote quantities immediately in front of and behind the wall, respectively), imply nontrivial relations between the bubble wall velocity ($V_\text{w}$) and the plasma velocity in front of the wall ($v_+$). Crucially, for deflagrations and hybrid solution regimes, $v_+$ can be much smaller than $V_\text{w}$ due to the formation of compression (sound) waves ahead of the expanding wall.

This hydrodynamic structure naturally decouples the wall velocity controlling GW production from the effective velocity relevant for baryogenesis, countering the often-assumed identification of these as a single parameter. For electroweak baryogenesis, the effective diffusion and conversion of CP asymmetries into baryon number are sensitive to $v_+$, which must satisfy $v_+ \lesssim D/L_w \sim 0.15$–$0.3$ (where $D$ is the CP charge diffusion constant and $L_w$ is the wall width) for efficient baryon production. In contrast, the GW signal from bubble collisions and bulk plasma motions is controlled by $V_\text{w}$, with

$$\Omega_{\text{GW}} h^2 \propto V_\text{w}^3 \, \kappa^2 \left(\frac{\alpha_N}{1 + \alpha_N}\right)^2$$

where $\kappa$ is the vacuum-energy conversion efficiency and $\alpha_N$ measures the strength of the transition.

Thus, strong GW signals are compatible with the subsonic $v_+$ required for baryogenesis, provided hydrodynamic effects are properly included (No, 2011).

2. Stochastic Gravitational Wave Backgrounds from Early-Universe Out-of-Equilibrium Phenomena

A wide range of early-universe processes, including first-order phase transitions, preheating, oscillon formation, and primordial black hole (PBH) scenarios, source stochastic GW backgrounds through the generation of time-dependent anisotropic stresses.

Key GW Sources and Their Features

Physical Mechanism	GW Source and Spectrum	Baryogenesis Link
First-order phase transitions	Bubble collisions, sound waves, turbulence ($\alpha$, $\beta$ dependent spectra; peak $f \propto T_*/v_w$)	Satisfies Sakharov out-of-eq.; wall regime crucial for CP diffusion
Oscillon formation post-inflation	Quadrupole anisotropies from non-spherical oscillons; spectrum peaks at oscillon frequency	Non-equilibrium dynamics facilitate baryogenesis
Primordial black hole evaporation	Scalar density (Poisson) fluctuations induce second-order tensor modes; unique GW spectral features	PBH decay produces heavy particles for "non-thermal" baryogenesis
Topological defect decay (e.g. cosmic strings)	GW bursts from cusp/kink events, with frequency spectrum sensitive to network evolution	Symmetry breaking scales coinciding with baryogenesis parameter choices

For instance, in finite-temperature transitions, the GW energy density produced by bubble collisions peaks at

$$\Omega_\text{GW} h^2(f_\text{coll}) \sim 10^{-6} \left(\frac{100}{g_*}\right)^{1/3} \left(\frac{H_*}{\beta}\right)^2 \kappa^2 \left(\frac{\alpha_N}{1+\alpha_N}\right)^2 \frac{1.84 V_\text{w}^3}{0.42 + V_\text{w}^2}$$

Oscillon-induced GW spectra are found to obey scaling relations with source amplitude $A$ and asymmetry parameter $\Delta$ as $\Omega_\text{GW} \propto A^4 \Delta^2$ (Antusch et al., 2017).

GW spectra from PBH scenarios can display double-peak features, with low-frequency peaks from inflationary adiabatic modes and high-frequency peaks from isocurvature fluctuations seeded by PBH formation, especially in an early matter-dominated era (Bhaumik et al., 2022).

3. Baryogenesis Mechanisms and Their Dynamical Interplay with GW Production

Baryogenesis models—such as electroweak baryogenesis, Affleck–Dine (AD) baryogenesis, or non-thermal PBH-induced baryogenesis—all require a departure from thermal equilibrium, B (or L) violation, and CP violation.

• Electroweak baryogenesis: Relies on CP-violating interactions at expanding phase transition walls and diffusion of CP asymmetries into the unbroken phase, where sphalerons are active. The efficiency of baryogenesis is set by $v_+$ and the wall thickness, not the overall wall velocity. Viable models often require tuning parameters (e.g., strong first-order phase transitions, extended scalar sectors) to simultaneously achieve a sufficient baryon asymmetry and an observable GW signal (No, 2011).
• Affleck–Dine baryogenesis: Proceeds via the generation of a large (complex) scalar ("AD field") VEV during inflation, which decays into quarks/leptons via A-term induced CP-violating phase rotation. The fragmentation of the AD condensate into Q-balls, and subsequent decay, is a potent source of gravitational waves, particularly if Q-balls dominate the energy density for a period or decay suddenly (Yu et al., 10 Apr 2025).
• PBH baryogenesis: Ultra-light PBHs, by complete Hawking evaporation before BBN, can produce heavy particles out of equilibrium, leading to baryogenesis through their decays. The stochastic GW signal reflects both the density perturbations from PBH formation (including Poissonian noise) and any cosmic string network generated by associated symmetry breaking (Datta et al., 2020, Barman et al., 2022).

The particular GW signature (frequency, amplitude, and possible spectral features such as double peaks or anisotropies) therefore encodes information about the baryogenesis process, the scale of new physics, and the nature of the early-universe transition.

4. Parameter Constraints, Experimental Prospects, and Indirect Probes

By measuring the amplitude and frequency of a stochastic GW background, future space-based and ground-based GW observatories—such as LISA, BBO, DECIGO, Cosmic Explorer, Einstein Telescope, or Pulsar Timing Arrays (PTAs)—can probe the underlying phase transition strength, duration, bubble wall properties, and thus the viability of baryogenesis scenarios.

• The GW amplitude and spectral peak locations depend on transition strength $\alpha$, duration parameter $\beta$, bubble wall velocity $V_\text{w}$, and latent heat conversion efficiency $\kappa$, with a typical "sweet spot" for detectability at strong but moderate transitions. Too strong supercooling or detonation-type walls may suppress the baryon asymmetry even if boosting the GW signal.
• In PBH scenarios, the mass window selected by baryogenesis (e.g., to emit GUT-scale particles or right-handed neutrinos before BBN) fixes the frequency range for the associated GW peak. GW signals in the mHz–kHz regime (LIGO, DECIGO, ET) correspond to PBH masses $\sim 10^4$–$10^7$ g. The shape—particularly doubly peaked GW spectra—serves as a smoking gun of non-thermal baryogenesis through PBH evaporation (Bhaumik et al., 2022).
• Measurement of GW anisotropies—characterized by a reduced angular power spectrum $\tilde{\mathcal{C}}_\ell \sim 10^{-2}$—would be a distinctive probe of non-Gaussian baryonic isocurvature perturbations arising in AD baryogenesis, revealing direct information about the CP-violating initial conditions at high energy scales (Yu et al., 10 Apr 2025).
• Collider constraints, electric dipole moment (EDM) bounds, and cosmological observations set further restrictions, especially on the available CP-violating phases and the possible strength of the phase transition.

In the presence of hydrodynamic decoupling, a detected large GW background from the electroweak phase transition does not exclude the possibility of electroweak baryogenesis, provided experimental measurements of v₊ (inferred from, e.g., transport modeling or related kinetic observables) are consistent with the subsonic regimes required for baryogenesis efficiency (No, 2011).

5. Theoretical and Computational Methodologies

Recent progress in this area relies on integrating several computational frameworks:

• Hydrodynamic modeling: Solving for bubble wall profiles (velocity and thickness) from first-principles microphysics; utilizing matching conditions and equation of state parameterizations (bag model, improved QCD EoS).
• Lattice simulations and semi-analytic formalisms: Used for GW production from oscillon fragmentation, AD field fragmentation, Q-ball formation, and FOPT bubble dynamics; providing concrete GW spectra and scaling behaviors validated against non-linear evolution.
• Regularization and renormalization: Development of time-dependent normal-ordering ("tNO") schemes in the computation of GW spectra from fermion production to handle UV divergences and ensure meaningful, physical results (Enqvist et al., 2012).
• Second-order cosmological perturbation theory: Relevant for computing GWs induced by scalar density fluctuations from PBH formation or eMD scenarios, often involving kernel integrals over the scalar power spectra and numerical solutions for the tensor evolution equations.

These methodologies are necessary for credible predictions of GW spectra and allow detailed mapping between particle physics model parameters and observable GW signals.

6. Interpretations, Challenges, and Future Prospects

Interpreting GW signals as signatures of baryogenesis mechanisms necessitates disentangling competing sources (astrophysical foregrounds, backgrounds from unrelated cosmological processes) and accounting for uncertainties in the modeling of phase transition hydrodynamics, non-linear scalar field dynamics, and cosmic string/pulsar timing analysis.

Challenges include:

• Accurate determination of the parameter space where baryogenesis and appreciable GW production coexist, especially given strict bounds on EDMs and collider limits on additional CP-violation.
• Reliable modeling of supercooled or super-strong transitions in which completed phase transitions may not be guaranteed, or where reheating effects damp energy available to GW production.
• Disentangling contributions to the GW background from primordial, non-thermal scenarios (e.g., PBHs, cosmic strings) versus those from late-time sources.

Future multi-messenger constraints—combining collider searches for new particles/couplings with GW signals and cosmological probes—are expected to sharply test the confluence of baryogenesis and stochastic GW production, offering the prospect of indirect access to mechanisms operating at energy scales well beyond terrestrial experiments.

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These developments establish stochastic gravitational wave signatures as a vital probe of baryogenesis scenarios—uniquely sensitive to early-universe phase transitions and out-of-equilibrium dynamics—marking an intersection of particle, astrophysical, and gravitational physics that is at the forefront of current and future observational campaigns.