Spontaneous Baryogenesis from Axions on Induced Electroweak Walls

This paper proposes a spontaneous baryogenesis mechanism where an axion-like particle coupled to the SU(2) Chern-Simons density induces an electroweak phase boundary via a moving scalar wall, generating a local chemical potential that biases unsuppressed sphaleron transitions to produce the observed baryon asymmetry while remaining consistent with current experimental bounds.

The Gist

The Big Mystery: Where Did All the Matter Come From?

Imagine the Big Bang as a giant explosion that created the universe. In a perfect world, this explosion should have created equal amounts of matter (the stuff we are made of) and antimatter (the "evil twin" that destroys matter on contact). If they were created equally, they would have annihilated each other instantly, leaving behind a universe filled only with light and no stars, planets, or people.

But here we are. We exist. This means something happened to tip the scales, creating a tiny bit more matter than antimatter. This is called Baryogenesis.

The Old Way vs. The New Idea

For decades, physicists have tried to explain this using a process called Electroweak Baryogenesis.

• The Old Analogy: Imagine a frozen lake (the early universe) slowly melting. As the ice melts, bubbles of water form. The scientists thought that as these bubbles grew, they acted like a sieve, letting more "good guys" (matter) through than "bad guys" (antimatter).
• The Problem: This old method requires very specific, fragile conditions. It's like trying to balance a pencil on its tip during an earthquake. It's hard to make work without breaking the laws of physics we already know.

The New Proposal: The "Moving Wall"

The authors of this paper propose a different, more flexible idea. Instead of bubbles forming in a melting lake, imagine a giant, moving wall sweeping across the universe.

Here is how their mechanism works, step-by-step:

1. The Invisible Wall (The Axion)

Imagine a field of invisible "axions" (a type of ghostly particle) filling the universe. Sometimes, these axions arrange themselves into a wall. Think of this wall like a front moving through a crowd. On one side of the wall, the axions are calm; on the other side, they are excited.

2. The "Switch" (The Higgs Field)

The Standard Model of physics has a field called the Higgs, which gives particles their mass. Usually, the Higgs field is "on" everywhere, giving particles mass.

• The Magic Trick: In this new theory, the moving Axion wall acts like a remote control switch for the Higgs field.
• Behind the wall: The Higgs is "off" (symmetric phase). Particles are massless and chaotic.
• In front of the wall: The Higgs is "on" (broken phase). Particles have mass and are stable.
• The Result: As the wall moves, it creates a sharp boundary where the laws of physics change instantly. This is the "Induced Electroweak Wall."

3. The "Chemical Potential" (The Tilted Floor)

This is the most important part. Because the wall is moving, it creates a sort of tilted floor for the particles.

• Imagine a ball rolling on a flat table. It goes nowhere.
• Now, imagine the table tilts slightly because the wall is pushing it. The ball naturally rolls in one direction.
• In physics terms, the moving wall creates an effective chemical potential. It's like a bias that tells the universe, "Hey, make a little more matter than antimatter right here, right now."

4. The "Freeze" (Sphalerons)

In the chaotic zone behind the wall (where the Higgs is off), there are wild energy fluctuations called sphalerons. These are like chaotic whirlpools that can swap matter for antimatter.

• Because of the "tilted floor" (the chemical potential), these whirlpools start producing more matter than antimatter.
• As the wall sweeps forward, the plasma (the hot soup of particles) crosses into the "safe zone" (where the Higgs is on).
• Once in the safe zone, the whirlpools stop working. The extra matter created is frozen in place. The universe keeps that extra matter.

Why Is This Better?

1. It's Local, Not Global: The old theories required the entire universe to be in a specific, high-energy state. This new theory only needs the wall to exist. It's like lighting a match in a dark room vs. trying to heat the whole room with a hairdryer.
2. It's Robust: It doesn't rely on the Higgs field doing something weird on its own. The wall forces the Higgs to behave.
3. It Solves the "Mess" Problem: If the wall moves too fast or too slow, the old theories fail. This new setup is forgiving; it works even if the wall moves at different speeds.

The "Smoking Gun": Gravitational Waves

If this happened, it wouldn't just be a theory; we could hear it.

• When these walls collapse or crash into each other, they would create ripples in space-time called Gravitational Waves.
• The authors predict these ripples would be loud enough for future detectors like LISA (a space-based gravitational wave observatory) to hear.
• The Analogy: If the Big Bang was a silent movie, this theory suggests there was a loud "crash" sound that we might finally be able to hear.

Summary

The paper suggests that the reason we exist (and not just light) is because a giant, moving wall of invisible particles swept through the early universe. This wall acted like a switch, turning on the Higgs field and tilting the playing field just enough to create a surplus of matter. This surplus got "frozen" in place, becoming the stars and galaxies we see today.

It's a clever, minimal solution that avoids the "pencil balancing" problems of older theories and offers a new way to test our universe's history with sound (gravitational waves).

Technical Summary

1. Problem Statement

The origin of the baryon asymmetry of the universe (BAU) remains a central open question. Conventional Electroweak Baryogenesis (EWBG) relies on a first-order electroweak phase transition (EWPT) driven by the Higgs potential, requiring:

• A strong first-order phase transition (often necessitating non-minimal Higgs sectors).
• CP-violating sources localized at the bubble wall.
• Specific wall velocities to allow chiral asymmetry diffusion before sphaleron washout.

These requirements often lead to tension with experimental constraints (e.g., Higgs coupling measurements, Electric Dipole Moments) and are sensitive to transport properties. Furthermore, standard Spontaneous Baryogenesis (where a time-dependent background field acts as a chemical potential) typically requires large, homogeneous kinetic energy densities throughout the universe, which can conflict with cosmological bounds.

The authors propose a mechanism to generate the BAU that avoids these pitfalls by utilizing induced electroweak walls created by a moving scalar field (axion-like particle), rather than a phase transition driven solely by the Higgs potential.

2. Methodology and Model Setup

A. Theoretical Framework

The model introduces a scalar field $\phi$ (identified as an axion-like particle, ALP) coupled to the Standard Model Higgs doublet $H$ and the $B+L$ current.

• Potential: The scalar potential is $V(H, \phi) = -m_H^2(\phi)|H|^2 + \lambda|H|^4 + V_\phi(\phi)$.
• Coupling: The Higgs mass parameter depends on $\phi$: $m_H^2(\phi) = \mu^2 + \lambda_P \phi^2 + A\phi$.
  • When $\phi$ takes a specific value (e.g., $\phi=v$), $m_H^2 < 0$, inducing the electroweak symmetry breaking (EWSB) phase.
  • When $\phi=0$, $m_H^2 > 0$, keeping the electroweak symmetry unbroken.
• Anomalous Coupling: The field $\phi$ couples to the $SU(2)$ Chern-Simons density (or equivalently the $B+L$ current) via:
  $$\delta \mathcal{L} = -c_{B+L} \frac{\partial_\mu \phi}{v} j^\mu_{B+L}$$
  In the plasma rest frame, the motion of the wall creates a time-dependent background $\dot{\phi}$, acting as an effective chemical potential for $B+L$:
  $$\mu_{B+L} = -c_{B+L} \frac{\dot{\phi}}{v}$$

B. The Mechanism: Induced Electroweak Walls

The core mechanism involves a "wall" (domain wall or shock wave) of the scalar field $\phi$ moving through the early universe plasma.

1. Induced Phase Boundary: As the wall passes, it locally changes the value of $\phi$. This induces a local transition in the Higgs sector: one side of the wall is in the symmetric phase ($\langle H \rangle = 0$), and the other is in the broken phase ($\langle H \rangle \neq 0$).
2. Sphaleron Bias:
   • Ahead of the wall (Symmetric Phase): Sphaleron transitions are active ($\Gamma_{sph} \sim T^4$). The effective chemical potential $\mu_{B+L}$ biases the thermal plasma, generating a non-zero $B+L$ density ($n_{B+L}^{eq} \propto \mu_{B+L} T^2$).
   • Behind the wall (Broken Phase): As the plasma crosses the wall, the Higgs VEV turns on, exponentially suppressing sphaleron transitions. The generated $B+L$ asymmetry is "frozen" and converted into a baryon asymmetry.
3. Local Nature: The large time variation of $\phi$ is confined to the wall vicinity. This relaxes the global energy density constraints associated with homogeneous spontaneous baryogenesis.

C. Scenarios Analyzed

The authors analyze two cosmological realizations:

1. Axionic Domain Walls: A network of domain walls formed by the ALP field. The network collapses due to a potential bias induced by the Higgs coupling.
2. Scalar Shock Waves: Expanding shock waves (e.g., from low-scale inflation) where the field $\phi$ transitions from a potential hilltop to a bottom, creating a transient bubble of broken symmetry.

3. Key Contributions

• Novel Mechanism: Proposes a "localized spontaneous baryogenesis" where the phase boundary is induced by the scalar wall's coupling to the Higgs, rather than being intrinsic to the Higgs potential.
• Relaxation of Constraints:
  • Avoids the need for a strong first-order EWPT driven by the Higgs sector.
  • Reduces sensitivity to CP-violating transport and wall velocity constraints typical of standard EWBG.
  • Alleviates constraints on homogeneous kinetic energy density.
• Inhomogeneity Control: Demonstrates that by tuning the collapse time of domain walls to occur near the electroweak scale ($T \sim 100$ GeV), the resulting baryon inhomogeneities are suppressed enough to satisfy Big Bang Nucleosynthesis (BBN) constraints (specifically the D/H ratio).
• Gravitational Wave (GW) Signatures: Predicts a stochastic gravitational wave background from the collapse of domain walls and the collision of shock waves, potentially observable by future detectors like LISA.

4. Results

A. Baryon Asymmetry Generation

• Analytic Estimate: The final baryon-to-entropy ratio is estimated as:
  $$\frac{n_B}{s} \sim 5 \times 10^{-8} \frac{\epsilon_1}{10.75/g_{*,\star}} \times \min\left[1, \frac{m_\phi \gamma_w}{10^{-6} T}\right]$$
  where $\epsilon_1$ is a numerical factor ($\sim 0.02 - 0.4$) derived from solving the Boltzmann equation.
• Numerical Validation: Numerical solutions of the Boltzmann equation confirm the analytic estimates, showing that the asymmetry saturates when the wall width is large compared to the sphaleron rate scale.
• Parameter Space:
  • Domain Walls: Requires an ALP mass $m_\phi \gtrsim 2.6$ GeV (to avoid dilution by muon/first-generation quark decays) and a decay constant $f_\phi \sim 10^9 - 10^{10}$ GeV. The reheating temperature must be $T_R > 0.1$ GeV to avoid excessive dilution.
  • Shock Waves: Allows for a broader parameter space, with viable regions accessible to beam-dump experiments (e.g., SHiP) and supernova constraints.

B. Gravitational Waves

• Domain Walls: The collapse of the domain wall network generates a GW signal with peak frequency $f_{peak} \sim \text{mHz}$ (within LISA's band) and amplitude $\Omega_{GW} h^2 \sim 10^{-7} - 10^{-9}$.
• Shock Waves: Expanding shock waves produce a distinct GW spectrum, also potentially detectable by LISA, MAGIS, or BBO.
• Dilution: The authors account for entropy dilution from the decay of the scalar field, which shifts the GW spectrum but leaves a detectable signal in specific parameter regions.

C. Comparison with Standard EWBG

• Appendix B Analysis: The authors show that standard EWBG sources (relying on CP-violating transport across the wall) are highly sensitive to wall velocity. Since wall velocity varies significantly during the collapse of a domain wall network, this leads to large spatial inhomogeneities in the baryon number, which are constrained by BBN. In contrast, the spontaneous baryogenesis mechanism proposed here is less sensitive to velocity variations, making it more robust.

5. Significance and Conclusion

This paper presents a minimal and flexible alternative to conventional electroweak baryogenesis. By decoupling the phase transition trigger from the Higgs potential and linking it to the dynamics of a light scalar field (axion), the mechanism:

1. Solves the "Strong CP" and "CP Violation" tension: It generates baryon asymmetry via a derivative coupling (spontaneous baryogenesis) rather than requiring large CP-violating phases in the Higgs sector, thereby evading stringent EDM bounds.
2. Provides a Testable Signature: Unlike many baryogenesis models that are purely theoretical, this scenario predicts a stochastic gravitational wave background in the mHz range, offering a direct observational test via space-based interferometers like LISA.
3. Connects Scales: It links the electroweak scale ($\sim 100$ GeV) with the axion scale ($f_\phi \sim 10^{10}$ GeV) and the mass of the ALP, providing a coherent cosmological history involving domain wall formation and collapse.

The work suggests that the baryon asymmetry could be a local phenomenon induced by topological defects or shock waves in the early universe, opening new avenues for exploring physics beyond the Standard Model through both cosmological observations and particle physics experiments.