Imprint of matter-antimatter asymmetry on collapsing domain walls

This paper proposes a novel mechanism where a large matter-antimatter asymmetry in Dirac fermions generates finite-temperature radiative corrections that destabilize cosmological domain walls, offering a unique pathway to probe the asymmetry's magnitude and generation temperature through future gravitational wave observations while potentially explaining baryon asymmetry, dark matter, and neutrino asymmetry.

The Gist

The Big Picture: A Cosmic Tug-of-War

Imagine the early universe as a giant, calm lake. Suddenly, a storm hits, and the water freezes into ice. But here's the catch: the ice doesn't freeze perfectly evenly. Some patches freeze with the "grain" of the water pointing up, and others point down.

In particle physics, this is called spontaneous symmetry breaking. When the universe cooled down, a field (let's call it the "Ice Field") settled into two different states. Where these two states meet, a boundary forms. In physics, we call these boundaries Domain Walls.

The Problem:
If these walls are stable, they are like heavy, invisible sheets stretching across the entire universe. They would act like a cosmic anchor, slowing down the expansion of the universe and eventually crushing everything. This is a "cosmological catastrophe." We know the universe didn't crash, so these walls must have disappeared.

The Usual Fix:
Usually, physicists say, "Let's just add a tiny little weight to one side of the scale." This is called a bias term. It makes one side of the wall slightly heavier than the other, causing the wall to crumble and collapse, releasing energy.

The New Idea in This Paper:
The authors (Dipendu Bhandari, Debasish Borah, and Indrajit Saha) propose a new way to add that weight. Instead of just randomly adding a weight, they say the weight comes from a crowd of particles that are unbalanced.

The Analogy: The Unbalanced Crowd

Imagine the Domain Wall is a giant, flexible trampoline stretched between two camps.

• Camp A represents "Matter."
• Camp B represents "Antimatter."

Normally, these camps have equal numbers of people. The trampoline is perfectly balanced and stays still.

But in this paper, the authors imagine a special type of particle (a Dirac Fermion) that shows up in huge numbers. However, there is a massive imbalance: for every 10 people in Camp A, there are only 9 in Camp B. Or even more extreme: 100 people in Camp A and 90 in Camp B.

This imbalance is called Asymmetry.

Because there are so many more people on one side, they push harder on the trampoline. This pressure difference (the bias) causes the trampoline to buckle, collapse, and snap.

The "Temperature" Twist

Here is the clever part of their discovery. The strength of this "push" depends on how hot the universe is at that moment.

• If the imbalance happens when the universe is very hot (early times), the particles are energetic and push hard.
• If it happens when the universe is cooler (later times), the push is weaker.

The authors found that if this imbalance is large enough (about 10% of the total particles, which is huge in physics terms), it creates enough pressure to make the domain walls collapse exactly when the imbalance is created.

The Result: A Cosmic Firework (Gravitational Waves)

When those giant domain walls collapse, they don't just disappear quietly. They crash into each other like colliding waves in a storm. This violent crash sends ripples through the fabric of space-time.

These ripples are Gravitational Waves (GWs).

Think of it like this:

• The Wall: A giant dam holding back a lake.
• The Imbalance: A sudden leak that makes the water level on one side drop.
• The Collapse: The dam breaks.
• The Sound: The roar of the water crashing down.

In our universe, that "roar" is a background hum of gravitational waves that we might be able to hear with future telescopes.

Why This Matters to Us

1. Detecting the Invisible: We can't see these domain walls, but we can "hear" them. The paper predicts exactly what frequency and loudness these waves would have. Future experiments like LISA (a space-based gravitational wave detector) or DECIGO might be able to detect this specific "hum."
2. A Time Machine: Because the strength of the signal depends on when the imbalance happened, detecting these waves would tell us not just that there was an imbalance, but when in the history of the universe it occurred. It's like finding a fossil that tells you exactly what year a dinosaur lived.
3. Solving Other Mysteries: The paper suggests that this huge imbalance of particles (10%!) might be the secret ingredient for other mysteries, like:
   • Dark Matter: Maybe the "missing" mass of the universe is made of these unbalanced particles.
   • Neutrinos: It could explain why neutrinos have mass or why there is more matter than antimatter in our visible universe.

Summary in One Sentence

The authors discovered that a massive, unbalanced crowd of invisible particles in the early universe could have pushed unstable cosmic "walls" to collapse, creating a unique sound (gravitational waves) that future telescopes might hear, revealing the secret history of how matter won over antimatter.

Technical Summary

1. Problem Statement

The spontaneous breaking of discrete symmetries (e.g., $Z_2$) in particle physics models often leads to the formation of Domain Walls (DWs). If these walls are stable, they quickly dominate the energy density of the Universe, leading to a cosmological catastrophe inconsistent with observations of the Cosmic Microwave Background (CMB) and Big Bang Nucleosynthesis (BBN).

To resolve this, the DW network must be made unstable to collapse before domination. This is typically achieved by introducing a bias term (an explicit symmetry-breaking term) in the scalar potential, creating a pressure difference that drives the walls to collapse and emit Stochastic Gravitational Waves (GWs).

The Gap: While bias terms are often introduced ad-hoc or attributed to high-scale quantum gravity operators, their specific origin and dependence on the thermal history of the Universe are not fully explored. Specifically, the link between the bias term and the particle-antiparticle asymmetry of fermions in the early Universe has not been systematically investigated as a primary driver for DW collapse.

2. Methodology

The authors propose a novel scenario where the bias term required for DW collapse is generated dynamically via radiative corrections from a degenerate Dirac fermion ($\chi$) with a large number density asymmetry.

• Model Setup:
  • A $Z_2$-odd scalar field $\phi$ with potential $V(\phi) = -\frac{\mu^2}{2}\phi^2 + \frac{\lambda}{4}\phi^4$.
  • Spontaneous symmetry breaking occurs at $v_\phi \simeq \sqrt{\mu^2/\lambda}$.
  • A vector-like Dirac fermion $\chi$ couples to $\phi$ via Yukawa interaction $-y\bar{\chi}\chi\phi$ and has a bare mass $m_0$. The field-dependent mass is $m_\chi(\phi) = m_0 + y\phi$.
• Bias Generation Mechanism:
  The bias term ($\Delta V$) arises from two sources:
  1. Zero-Temperature ($T=0$): Coleman-Weinberg radiative corrections. This contribution is independent of asymmetry.
  2. Finite-Temperature ($T>0$): Thermal corrections dependent on the chemical potential ($\mu$) of the fermion $\chi$. This contribution is directly proportional to the asymmetry ($Y_{\Delta\chi}$) in the number density of $\chi$.
• Analytical Approach:
  • The authors derive the finite-temperature potential correction $V_T$ including the chemical potential $\mu$, utilizing PolyLog functions ($Li_2$) and Bessel functions.
  • They calculate the bias term $\Delta V_T = V_T(+v_\phi) - V_T(-v_\phi)$.
  • They equate the pressure difference (bias) with the domain wall tension force to determine the annihilation temperature ($T_{ann}$).
  • They map the parameter space ($y$ vs. $m_0$) considering constraints from BBN, CMB ($N_{eff}$), and future GW detectors.

3. Key Contributions

• Novel Origin of Bias: The paper establishes a direct link between the bias term driving DW collapse and the chemical potential/asymmetry of a Dirac fermion. This provides a physical origin for the bias rather than an ad-hoc addition.
• Dominance of Finite-Temperature Effects: The authors identify a specific region of parameter space where the asymmetry-dependent finite-temperature bias dominates over the zero-temperature Coleman-Weinberg bias.
• Dual Probing Mechanism: The scenario allows for the simultaneous probing of:
  1. The magnitude of the asymmetry ($Y_{\Delta\chi}$).
  2. The temperature of asymmetry generation/injection ($T_{inj}$).
     Both parameters uniquely determine the peak frequency and amplitude of the resulting GW spectrum.
• Resolution of the DW Problem: The study demonstrates that a large asymmetry ($\sim O(0.1)$) in the Dirac fermion sector can naturally destabilize the DW network, avoiding the cosmological catastrophe while producing observable GWs.

4. Results

• Gravitational Wave Signatures:
  • The collapse of DWs produces a stochastic GW background.
  • Peak Frequency ($f_{peak}$): Determined by the annihilation temperature $T_{ann}$. Higher injection temperatures ($T_{inj}$) lead to earlier annihilation and higher GW frequencies.
  • Peak Amplitude ($\Omega_{GW}h^2$): Directly correlated with the magnitude of the asymmetry. Larger asymmetry leads to a stronger bias, faster collapse, and higher GW amplitude.
• Parameter Space Constraints:
  • Viable Regions: The study identifies viable regions in the $y-m_0$ plane for symmetry breaking scales $v_\phi = 10^4, 10^6, 10^8, 10^{10}$ GeV.
  • Experimental Reach: A significant portion of the parameter space is accessible to future experiments:
    • LISA, DECIGO, ARES, THEIA: Sensitive to the GW peak.
    • CMB-HD: Sensitive to the enhanced dark radiation ($\Delta N_{eff}$) caused by the GW energy density.
  • Constraints:
    • BBN: $T_{ann}$ must be $> T_{BBN}$ to preserve light element abundances.
    • CMB ($N_{eff}$): The GW energy density must not exceed Planck 2018 bounds on effective relativistic degrees of freedom.
• Asymmetry Magnitude: The model requires a comoving asymmetry $Y_{\Delta\chi} \sim O(0.1)$. While this is much larger than the baryon asymmetry ($\sim 10^{-10}$), it is consistent with scenarios involving Asymmetric Dark Matter or Large Neutrino Asymmetry.

5. Significance and Implications

• Observational Window: This work provides a unique "smoking gun" for detecting matter-antimatter asymmetry in the dark sector. Unlike standard baryogenesis, which is hard to probe directly, the collapse of domain walls induced by this asymmetry leaves a distinct imprint in the GW spectrum.
• Connection to Dark Matter and Neutrinos:
  • The large asymmetry stored in the singlet Dirac fermion $\chi$ can be transferred to neutrinos (via seesaw decays), potentially explaining the Helium anomaly and enhancing $N_{eff}$.
  • It offers a mechanism for Cogenesis, where the decay of $\chi$ generates both the baryon asymmetry and asymmetric dark matter.
• Theoretical Framework: The paper moves beyond ad-hoc bias terms, grounding the instability of domain walls in finite-temperature field theory and the thermodynamics of the early Universe.
• Future Directions: The authors suggest that the origin of such a large asymmetry could be explained by the Affleck-Dine mechanism, opening avenues for UV-complete models.

In summary, the paper proposes that the "imprint" of a large matter-antimatter asymmetry in a hidden fermion sector can be detected via the specific frequency and amplitude of gravitational waves generated by the collapse of unstable domain walls, offering a new observational probe for early Universe physics.