Particle-antiparticle perturbation mode horizon crossing: baryogenesis, leptogenesis and magnetogenesis

This paper proposes that during the reheating epoch, horizon-crossing perturbations in gravitationally produced particle-antiparticle pairs generate matter-antimatter asymmetries that simultaneously explain baryogenesis, leptogenesis, and magnetogenesis while also accounting for dark matter asymmetry, with results consistent with observational data.

The Gist

The Big Mystery: Why is there "Stuff" and no "Anti-Stuff"?

Imagine the universe began as a perfect, blank canvas. According to the laws of physics, when you create something, you should create its opposite at the same time. If you make a particle of matter (like a proton), you should also make a particle of "anti-matter" (an anti-proton). They are like perfect mirror images: if they meet, they annihilate each other and disappear into pure energy.

If the universe started this way, everything should have cancelled out. We should be living in a sea of empty light, with no stars, no planets, and no us. But that's not the case. We are here. There is matter everywhere, and almost no anti-matter.

The Question: Where did the extra matter come from? Why did the mirror break?

The Paper's Solution: The "Freezing" of a Ripple

The author, She-Sheng Xue, proposes a new way to solve this mystery. He suggests that the imbalance didn't happen because the laws of physics were broken (which would be like a magic trick). Instead, it happened because of timing and distance.

Here is the story in three acts:

Act 1: The Great Dance (Reheating)

Imagine the universe right after the Big Bang. It was a chaotic, super-hot soup. During a phase called "reheating," heavy, unstable particles (let's call them "Giant Dancers") were being created and then quickly decaying into the lighter particles we know today (like protons and electrons).

Normally, these Giant Dancers come in pairs: one matter, one anti-matter. They dance together, perfectly synchronized.

Act 2: The Horizon (The Invisible Wall)

In cosmology, there is a concept called the Horizon. Think of the horizon as a giant, expanding bubble of visibility. Nothing can travel faster than light, so if two things are outside each other's horizon, they can't "see" or "talk" to each other. They are causally disconnected.

The paper suggests that the Giant Dancers weren't just dancing randomly; they were creating ripples in their density (some areas had more dancers, some had fewer).

• Scenario A (Small Ripple): If the ripple is small (smaller than the horizon bubble), the matter and anti-matter can still talk to each other. They can swap places and cancel out the differences. The net result is zero.
• Scenario B (Big Ripple): If the ripple is larger than the horizon bubble, the two sides of the ripple get separated by the "wall." One side of the ripple is inside the bubble; the other side is outside.

Act 3: The Freeze (Superhorizon Crossing)

This is the magic moment. When the ripple gets bigger than the horizon, the two sides get frozen in place relative to each other. They can no longer communicate to cancel out their differences.

Imagine you have a bucket of red and blue paint mixed together. If you stir it, it becomes purple (balanced). But if you suddenly freeze the bucket so fast that the red paint is on the left and the blue paint is on the right, and you can't stir them anymore, you end up with a permanent imbalance.

In the universe, this "freezing" happened. Inside our observable universe (the horizon), there ended up being slightly more "matter" dancers than "anti-matter" dancers. The "anti-matter" dancers were stuck outside the horizon, frozen in a different patch of the universe.

The Result: A Three-For-One Deal

Once this imbalance was frozen in, the Giant Dancers started to die (decay) into the particles we see today. Because there were more "matter" dancers than "anti-matter" dancers inside our bubble, the decay produced:

1. Baryogenesis: More protons and neutrons (matter) than anti-protons.
2. Leptogenesis: More electrons (matter) than anti-electrons.
3. Dark Matter Asymmetry: A similar imbalance for the mysterious "dark matter" that holds galaxies together.

The paper calculates that the amount of extra matter produced matches exactly what we observe in the universe today.

The Bonus: Creating Magnetic Fields (Magnetogenesis)

Here is the clever twist. The paper explains how this process also created the magnetic fields that exist in space today.

• The Analogy: Imagine a crowd of people running. If everyone runs at the exact same speed in the exact same direction, there is no "traffic jam" or "wind."
• The Reality: In this scenario, the heavy particles decayed into protons (heavy) and electrons (light). Because they have different masses, they couldn't run at the same speed even if they wanted to. The electrons zoomed away faster; the protons lumbered behind.
• The Current: This difference in speed created a "traffic flow" of electric charge. In physics, moving electric charges create electric currents.
• The Magnetism: Wherever you have an electric current, you get a magnetic field.

So, the simple fact that protons and electrons move at different speeds created a giant electric current in the early universe, which generated the primordial magnetic fields we see in galaxies today.

Why This Matters

1. No Magic Needed: This theory doesn't require breaking the fundamental laws of physics (CPT symmetry). It just uses the geometry of the universe (horizons) and the timing of events.
2. Everything is Connected: It links three huge mysteries—why we have matter, why we have leptons, and why the universe has magnetic fields—into one single event: the "freezing" of a ripple during the universe's reheating phase.
3. It Fits the Data: The math works out. The predicted amount of matter and the strength of the magnetic fields match what astronomers actually observe in the sky today.

Summary in One Sentence

The universe didn't start with a bias toward matter; it started with a perfect balance, but a cosmic "freeze" separated the matter from the anti-matter, leaving us with a surplus of stuff and a side effect of magnetic fields.

Technical Summary

1. Problem Statement

The paper addresses three fundamental mysteries in cosmology and particle physics:

1. Baryogenesis and Leptogenesis: The observed dominance of matter over antimatter in the Universe (specifically the baryon-to-entropy ratio $n_B/s \approx 8.64 \times 10^{-11}$) remains unexplained within the Standard Model (SM) without invoking significant CPT violation or specific dynamical mechanisms (like electroweak phase transitions) that often fail to match observational data.
2. Magnetogenesis: The origin of primordial magnetic fields (PMFs) observed in galaxies and galaxy clusters, which have lower bounds ($B > 10^{-17}$ G) and upper bounds ($B < 10^{-9}$ G) on megaparsec scales.
3. Dark Matter Asymmetry: The potential asymmetry between dark matter particles and anti-dark matter particles.

The author challenges the standard paradigm where initial particle-antiparticle asymmetry is zero and must be generated dynamically via CPT-violating interactions. Instead, the paper proposes that the asymmetry arises naturally from horizon crossing dynamics during the reheating epoch, without violating fundamental CPT symmetry.

2. Methodology

The study utilizes a $\tilde{\Lambda}$CDM cosmological model involving a time-varying cosmological term and gravitationally produced massive particle-antiparticle pairs ($X$ and $\bar{X}$). The methodology proceeds through the following steps:

• Gravitational Production: Massive particles $X$ and $\bar{X}$ are produced in pairs during the inflation/reheating transition, preserving global CPT symmetry (total net number is zero).
• Perturbation Mode Analysis: The paper analyzes density contrast perturbations ($\delta_M$) between particles and antiparticles.
  • Sub-horizon modes: If the perturbation wavelength is smaller than the Hubble radius, local differences average to zero.
  • Super-horizon modes: If the perturbation wavelength exceeds the Hubble radius, the modes "freeze out" and decouple from microphysics. This prevents the local particle-antiparticle density difference from averaging to zero, creating a net asymmetry inside the horizon.
• Reheating Dynamics: The unstable massive particles $X$ decay into Standard Model (SM) baryons ($B$) and leptons ($L$), as well as dark matter particles ($D$). The decay preserves $B-L$ symmetry.
• Current Generation: The paper calculates the electric current generated by the decay products. Since baryons and leptons have different masses, their kinematic velocities ($\vec{v}_B$ and $\vec{v}_L$) differ even if produced in the same decay event, leading to a non-vanishing net electric current.
• Maxwell Equations: The generated current is used in the integral form of Maxwell's equations to derive the strength of the resulting primordial magnetic field.

3. Key Contributions

• Horizon Crossing Mechanism for Asymmetry: The paper proposes a novel mechanism where particle-antiparticle asymmetry is a geometric consequence of super-horizon mode freezing during reheating, rather than a result of explicit CPT violation in the Lagrangian. This bypasses the need for the Sakharov conditions (specifically the requirement for CPT violation) in the standard dynamical sense.
• Unified Origin of Baryogenesis, Leptogenesis, and Magnetogenesis: It demonstrates that these three phenomena are intrinsically linked. The horizon crossing creates a net particle excess; the decay of this excess creates baryon/lepton asymmetry; the kinematic difference in the decay products creates an electric current; and this current generates primordial magnetic fields.
• Quantitative Constraints: The author derives specific analytical expressions for the baryon/lepton-to-entropy ratios and the upper/lower bounds of the primordial magnetic field, linking them to the mass scale of the decaying particles ($\hat{m}$) and the reheating temperature ($T_{RH}$).

4. Key Results

The paper presents the following quantitative findings based on the $\tilde{\Lambda}$CDM model:

• Baryon and Lepton Asymmetry:

  • The net baryon and lepton number densities are derived from the frozen perturbation amplitude $\bar{\delta}^{crout}_M \approx 2.31 \times 10^{-4}$.
  • The resulting baryon-to-entropy ratio is calculated as:
    $$\frac{n_B}{s} \approx 2.6 \times 10^{-4} \frac{T_{RH}}{\hat{m}}$$
  • Matching the observational value ($n_B/s \approx 0.864 \times 10^{-10}$) constrains the ratio $T_{RH}/\hat{m} \approx 3.3 \times 10^{-7}$.
  • Due to $B-L$ symmetry, the lepton-to-entropy ratio is comparable to the baryon ratio ($n_L/s \sim n_B/s$).

• Charged vs. Neutral Components:

  • The paper argues that due to $\beta$-equilibrium and charge neutrality, the charged baryon and lepton densities are roughly half the total densities ($n_{Bc} \approx n_{B0} \approx n_B/2$).
  • This ensures that the charged components required for current generation are significant.

• Primordial Magnetic Field (PMF) Bounds:

  • Using the electric current density $\vec{j}_R = e(\vec{v}_B - \vec{v}_L)n_{Bc}$, the paper calculates the magnetic field $B_0$ observed today.
  • Upper Limit: Assuming maximal relative velocity ($|\vec{v}_B - \vec{v}_L| \approx c$), the upper bound is:
    $$B_0 < 4.48 \times 10^{-12} \text{ Gauss}$$
    (Consistent with the CMB upper limit of $10^{-9}$ G).
  • Lower Limit: Assuming minimal relative velocity derived from the perturbation gradient, the lower bound is:
    $$B_0 > 6.9 \times 10^{-16} \text{ Gauss}$$
    (Consistent with the intergalactic lower limit of $10^{-17}$ G).
  • The final theoretical range is $4.48 \times 10^{-12} > B_0 > 6.9 \times 10^{-16}$ Gauss.

• Dark Matter: The framework also predicts an asymmetry between dark matter and anti-dark matter, though the magnitude depends on the dark sector Yukawa coupling ($g_Y^D$), which is expected to be larger than the SM coupling to explain the dominance of dark matter.

5. Significance

• Resolution of the Asymmetry Problem: The paper offers a solution to the matter-antimatter asymmetry that relies on standard cosmological expansion and horizon physics rather than exotic CPT-violating physics, preserving the fundamental symmetry of the Lagrangian.
• Explaining Primordial Magnetism: It provides a natural, causal mechanism for the generation of primordial magnetic fields, linking them directly to the baryogenesis process. This resolves the "seed field" problem for galactic dynamos.
• Observational Consistency: The derived bounds for the primordial magnetic field and the baryon-to-entropy ratio fall squarely within current observational constraints, validating the model's viability.
• Theoretical Unification: The work suggests that baryogenesis, leptogenesis, and magnetogenesis are not independent phenomena but different facets of the same horizon-crossing event during the reheating epoch.

In conclusion, She-Sheng Xue presents a coherent theoretical framework where the geometric evolution of the Universe (horizon crossing) during reheating naturally seeds the matter-antimatter asymmetry and the primordial magnetic fields observed today, all while maintaining CPT symmetry.