⚛️ phenomenology

Baryogenesis and CMB spectral distortion from Axions

This paper proposes a mechanism where axion-like particles modify Standard Model gauge field configurations to generate the observed baryon asymmetry and produce a unique, constant low-frequency Cosmic Microwave Background spectral distortion distinct from conventional y-type and $\mu$ -type distortions.

Original authors: Zhenhao Zhang, Mingqiu Li, Sichun Sun

Published 2026-08-12

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CC BY 4.0

Original authors: Zhenhao Zhang, Mingqiu Li, Sichun Sun

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, expanding balloon that was once incredibly hot and dense. In the very first moments after the "Big Bang," a cosmic mystery unfolded: why does our universe contain almost entirely matter (the stuff that makes up stars, planets, and us) instead of an equal mix of matter and antimatter? If they had been created in perfect balance, they would have annihilated each other, leaving behind only a sea of light. But they didn't. Something tipped the scales. This imbalance is called "baryon asymmetry," and figuring out how it happened is one of the biggest puzzles in physics. To solve it, scientists look for tiny, invisible particles that might have nudged the universe in the right direction. One such candidate is the "axion," a ghostly particle originally proposed to solve a different problem but now suspected of being a key player in the early universe's drama. The question is: could these axions have been the referees that called the foul, creating the extra matter we see today?

This paper explores a specific, playful scenario where axions act as cosmic conductors, changing the rhythm of invisible force fields to create more matter than antimatter. The authors, Zhenhao Zhang, Mingqiu Li, and Sichun Sun, propose that an axion-like particle (ALP) moving through the early universe could twist the behavior of electromagnetic fields. Think of the universe's force fields as a calm lake. Usually, waves on this lake move at the same speed regardless of their direction. However, the authors suggest that a moving axion acts like a strong wind blowing across the surface, making waves traveling one way move slightly faster than waves traveling the other way. This difference in speed creates a "handedness" or twist in the fields. In the language of physics, this twist changes a quantity called the "Chern-Simons number," which, according to the rules of the Standard Model, forces the universe to create more baryons (protons and neutrons) than anti-baryons.

The researchers calculated how much matter this mechanism could produce and found that the answer depends heavily on how the axion is moving. They tested two main scenarios. The first is the "traditional misalignment mechanism," where the axion field starts at a high point and slowly rolls down to a valley. The authors suggest that in this slow-rolling scenario, the axion doesn't move fast enough to generate the massive amount of matter we observe in the universe today; it's like trying to fill a swimming pool with a dripping faucet. However, they found a much more promising path: the "kinetic misalignment mechanism." In this version, the axion is zooming through the universe with high speed, like a race car, before it even starts to slow down. The authors show that if the axion is moving fast enough in this "kinetic" state, it can naturally produce the exact amount of matter asymmetry we see today, provided the universe was hot enough when this process started (between $10^5$ and $10^7$ GeV).

But the story doesn't end with just creating matter. The authors also looked at what happens to light in this scenario. They suggest that the same axion wind that twists the force fields also changes how light waves travel. Usually, light of all colors travels at the same speed, but the axion background could make different colors of light travel at slightly different speeds. This would leave a unique fingerprint on the Cosmic Microwave Background (CMB), the afterglow of the Big Bang. The authors estimate that this effect would create a specific type of "spectral distortion"—a wobble in the energy spectrum of the CMB. Unlike the familiar distortions caused by heat or scattering (known as $\mu$ and $y$ types), this axion-induced distortion would look like a flat, constant bump at low frequencies. While the authors suggest this signal is likely too faint to detect with current technology due to the weak connection between axions and photons, the shape of the signal is unique. It offers a new way to hunt for these invisible particles: if we ever see this specific, flat-bottomed distortion in the cosmic background, it could be the smoking gun for axions, proving they were the architects of our matter-filled universe.

Technical Summary: Baryogenesis and CMB Spectral Distortion from Axions

Problem Statement
The origin of the baryon asymmetry of the universe (BAU), characterized by the ratio $n_B/s \approx 9 \times 10^{-11}$ , remains an unresolved mystery in cosmology. While various mechanisms such as electroweak baryogenesis and leptogenesis have been proposed, none have been experimentally confirmed. Furthermore, standard inflationary scenarios typically dilute any pre-existing asymmetry, necessitating a generation mechanism post-inflation. Concurrently, the Cosmic Microwave Background (CMB) spectrum is expected to be a perfect blackbody, yet deviations (spectral distortions) can arise from energy injection or extraction in the early universe. The authors investigate whether Axion-Like Particles (ALPs) can simultaneously address the BAU and induce distinct CMB spectral distortions through their coupling to Standard Model gauge fields.

Methodology
The authors propose a mechanism where an ALP background modifies the gauge field configurations of the Standard Model, specifically focusing on the $U(1)_Y$ hypercharge field. The study proceeds through the following steps:

Lagrangian and Dispersion Relations: The authors introduce a Chern-Simons coupling between the ALP field $\phi$ and the $U(1)_Y$ field strength $Y_{\mu\nu}$ . In an expanding universe, this coupling alters the dispersion relations for the two circular polarization modes of the gauge field, leading to a frequency shift dependent on the axion velocity $\dot{\phi}$ .
Thermal Equilibrium Assumption: Unlike previous models that rely on complex non-equilibrium dynamics, this work assumes the gauge fields remain in thermal equilibrium. The authors derive the distribution functions for the gauge bosons under the modified dispersion relations, treating the axion background as homogeneous.
Anomaly Equation Integration: Using the Standard Model anomaly equation $\partial_\mu J^\mu_B = -\frac{N_F g_Y^2}{32\pi^2} Y_{\mu\nu}\tilde{Y}^{\mu\nu}$ , the authors relate the change in baryon number to the expectation value $\langle E \cdot B \rangle$ . They derive an analytical relationship between the baryon number density and the evolution of the axion background ( $\dot{\phi}/T$ ).
Scenario Analysis: The baryogenesis potential is evaluated under two distinct axion evolution scenarios:
- Traditional Misalignment Mechanism: The axion field starts with a non-zero value and oscillates around the potential minimum.
- Kinetic Misalignment Mechanism: The axion possesses sufficient initial kinetic energy to overcome the potential barrier, maintaining a non-zero velocity $\dot{\phi}$ over a longer duration.
CMB Distortion Calculation: Post-electroweak phase transition, the coupling reduces to the axion-photon interaction. The authors calculate the resulting modification to the photon distribution function and the induced spectral distortion $\delta I(\nu)$ , comparing it against standard $\mu$ -type and $y$ -type distortions.

Key Contributions and Results

Baryogenesis via Kinetic Misalignment:
- The authors demonstrate that the traditional misalignment mechanism fails to produce the observed baryon asymmetry ( $n_B/s \sim 10^{-10}$ ). For light axions ( $m \lesssim 1.1 \times 10^{-4}$ eV), the velocity $\dot{\phi}$ is too small; for heavier axions, the field oscillates before the electroweak phase transition, causing spatial inhomogeneities that average the baryon production to zero.
- Conversely, the kinetic misalignment mechanism successfully generates the required asymmetry. The final baryon asymmetry is proportional to the conserved Peccei-Quinn charge normalized by entropy ( $Y_{PQ}$ ), the coupling $\beta_1$ , and the temperature difference between the start ( $T_i$ ) and end ( $T_f$ ) of the mechanism.
- Parameter scans indicate that for axion decay constants $10^8 \text{ GeV} < f_a < 10^{11} \text{ GeV}$ and initial temperatures $10^5 \text{ GeV} < T_i < 10^7 \text{ GeV}$ , the model naturally achieves $n_B/s \approx 10^{-10}$ while satisfying constraints from the Cosmic Axion Solar Telescope (CAST) and dark matter abundance ( $\Omega_a = \Omega_{DM}$ ).
Distinct CMB Spectral Distortion:
- The axion-photon coupling alters the photon dispersion relation, leading to a spectral distortion in the CMB.
- A critical finding is the frequency dependence of this distortion. Unlike conventional $\mu$ -type and $y$ -type distortions, which vanish at low frequencies, the axion-induced distortion $\delta I_a(\nu)$ approaches a constant non-zero value ( $\epsilon^2 I_0$ ) at low frequencies.
- However, the authors note that due to the weak coupling ( $g_{a\gamma\gamma} \sim 10^{-10} \text{ GeV}^{-1}$ ), the magnitude of this distortion is extremely small ( $\epsilon^2 \sim 10^{-5}$ ), making it currently difficult to detect with existing instruments like COBE/FIRAS.

Significance and Claims
The paper claims to provide a unified framework where ALPs generate baryon asymmetry without violating Sakharov's conditions in the traditional sense, as the CPT violation arises from the non-vanishing velocity of the classical axion field. The primary significance lies in identifying the kinetic misalignment mechanism as a viable pathway for axion-induced baryogenesis, which the traditional mechanism cannot support.

Furthermore, the work highlights a unique observational signature: a low-frequency constant plateau in CMB spectral distortions. While the authors acknowledge the current difficulty in detecting this signal due to faint couplings, they assert that this distinct shape offers a new theoretical handle for studying Chern-Simons couplings to photons. The study concludes that while the model is effective for baryogenesis, the associated CMB distortion remains a subtle effect, and the Standard Model in this context acts as an effective theory valid below the initial temperature $T_i$ of the baryogenesis epoch.

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