⚛️ phenomenology

Spontaneous Cogensis by QCD axion in Type I Seesaw

This paper proposes a generic axion-driven cogenesis scenario within a Type-I seesaw and DFSZ framework, where Hubble-induced masses and PQ-violating operators trigger early axion rotation to simultaneously generate the baryon asymmetry and dark matter abundance via kinetic misalignment, all while satisfying strong CP constraints and isocurvature limits.

Original authors: Eung Jin Chun

Published 2026-01-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Eung Jin Chun

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

The Big Picture: Solving Two Mysteries at Once

Imagine the universe has two massive, unsolved mysteries:

The Missing Matter: We know there is invisible "Dark Matter" holding galaxies together, but we don't know what it is.
The Missing Antimatter: The Big Bang should have created equal amounts of matter and antimatter, which would have destroyed each other. Yet, we exist. There is way more matter than antimatter.

Usually, physicists try to solve these problems separately. This paper proposes a "two-for-one deal." It suggests that a single, tiny particle called the Axion (a candidate for Dark Matter) is also the engine that created the extra matter we see today. The author calls this "Cogenesis" (creating both at the same time).

The Main Characters

To understand the story, we need to meet the cast:

The Axion: A ghost-like, ultra-light particle. Think of it as a tiny, invisible spinning top.
The Heavy Neutrino: A super-heavy cousin of the neutrino (a particle we know exists). Think of it as a heavy, unstable boulder that eventually breaks apart.
The "Hubble" Force: A force related to the expansion of the universe, acting like a giant wind or friction.
The "PQ" Symmetry: A hidden rule of nature that, when broken, creates the Axion.

The Story: How It Works

1. The Setup: A Spinning Top in a Frictionless Room

In the very early universe, right after the Big Bang, the Axion field was like a spinning top. Usually, these tops just sit still. But in this scenario, the universe gave the top a massive initial spin (called "kinetic misalignment").

Imagine a child pushing a spinning top so hard that it starts whirling around a room. This spinning motion is the "kinetic misalignment."

2. The Engine: The Spin Creates Matter

As this Axion top spins, it interacts with the heavy neutrinos (the boulders).

The Analogy: Imagine the spinning top is a giant fan. As it spins, it blows air (energy) at the heavy boulders.
The Result: The heavy neutrinos get pushed and eventually break apart (decay). Because the fan (the Axion) is spinning in a specific direction, it pushes the debris of the broken boulders in a way that creates more matter than antimatter.
The Paper's Claim: The speed of the Axion's spin ( $\dot{\theta}$ ) directly determines how much extra matter is created. If the spin is just right, we get exactly the amount of matter we see in the universe today.

3. The Aftermath: The Top Becomes Dark Matter

Once the heavy neutrinos have done their job and the universe has cooled down, the Axion top slows down. It stops spinning wildly and starts to wobble gently in place.

The Analogy: The spinning fan slows down until it's just a stationary object sitting in the room.
The Result: This "wobbling" Axion is stable and invisible. It doesn't decay. It becomes the Dark Matter that fills the universe.

So, the same Axion that spun fast to create our matter (Baryogenesis) eventually slowed down to become the Dark Matter (Cogenesis).

The Mechanics: How Did the Spin Start?

The paper addresses a tricky question: How did the Axion get that initial spin in the first place?

In many old theories, the Axion was tied to the "Inflation" (the rapid expansion of the universe), which made the theory very rigid and limited. This paper proposes a more flexible setup:

The Hubble Kick: The expansion of the universe itself (the Hubble force) gave the Axion field a "kick" early on, ensuring it was broken and ready to spin.
The Nudge: A tiny, higher-dimensional "nudge" (a small violation of symmetry) acted like a slight tilt in the floor, causing the Axion to start rolling and spinning.

The Rules of the Game (Constraints)

The author didn't just make up a story; they checked if it fits the rules of physics:

The Strong CP Problem: The Axion was originally invented to solve a different problem (why the strong nuclear force doesn't break symmetry). The paper shows this new spinning scenario doesn't break that original solution.
The "Quality" Check: The "nudge" that started the spin must be very small, or else it would ruin the Axion's ability to solve the Strong CP problem. The paper calculates exactly how small this nudge needs to be.
The "Isocurvature" Limit: If the Axion field was too wild during the early universe, it would leave "scars" (ripples) in the Cosmic Microwave Background (the afterglow of the Big Bang). The paper shows that their model keeps these scars small enough to match what telescopes see today.

The Conclusion: A Sweet Spot

The paper identifies a "Goldilocks zone" for the mass of the heavy neutrinos.

If the neutrinos are too light or too heavy, the math doesn't work, and we wouldn't have the right amount of matter or dark matter.
The author calculates that for the Axion to work as both the matter-creator and the dark matter, the heavy neutrinos must have a mass roughly between 10 and 100 TeV (depending on the specific properties of the Axion).

In summary: This paper proposes that the universe is like a clockwork mechanism where a single spinning part (the Axion) winds up to create the matter we are made of, and then settles down to become the invisible scaffolding (Dark Matter) holding the universe together. It unifies the solution to the Strong CP problem, the origin of neutrino masses, and the creation of the universe's matter and dark matter into one elegant, spinning story.

Technical Summary: Spontaneous Cogenesis by QCD Axion in Type I Seesaw

Problem Statement
The paper addresses the simultaneous origin of the baryon asymmetry of the universe (BAU) and dark matter (DM) abundance, a scenario known as "cogenesis." While the Peccei–Quinn (PQ) mechanism is the leading solution to the strong CP problem and axions are well-motivated DM candidates, the physical origin of the required initial kinetic misalignment (axion rotation, $\dot{\theta}$ ) remains an unresolved issue in standard scenarios. Previous proposals, such as identifying the PQ field as the inflaton, are often highly restrictive (e.g., limited to KSVZ models and narrow axion decay constant ranges). Furthermore, unifying the PQ mechanism with the Type-I seesaw mechanism for neutrino mass generation while generating both BAU and DM via kinetic misalignment without relying on specific inflationary microphysics is a significant theoretical challenge.

Methodology
The authors propose a unified framework within the DFSZ axion model augmented by heavy right-handed neutrinos (Type-I seesaw). The methodology involves:

Lagrangian Construction: Defining a Lagrangian where the PQ scalar $\Phi$ couples to two Higgs doublets ( $H_u, H_d$ ) and right-handed neutrinos ( $N$ ). The PQ charges are assigned to ensure the axion solves the strong CP problem while allowing for neutrino mass generation ( $m_N = y_N v_a / \sqrt{2}$ ).
Chemical Potential Analysis: Deriving the relations between chemical potentials in the presence of a kinetic background $\dot{\theta}$ . By assuming equilibrium for interactions (including neutrino decays) and enforcing charge neutrality, the authors calculate the resulting $B-L$ and baryon number densities ( $n_B$ ) as functions of $\dot{\theta}$ and temperature $T$ .
Kinetic Misalignment Generation: Modeling the PQ symmetry breaking during inflation using a scalar potential with a Hubble-induced mass term ( $a_H H^2$ ) to ensure symmetry remains broken (avoiding domain wall problems). To trigger the necessary axion rotation, a higher-dimensional PQ-violating (PQV) operator is introduced. The evolution of the axion field is analyzed from the end of inflation through the matter-dominated era to the onset of radiation domination.
Parameter Space Constraints: The viable parameter space is determined by imposing constraints from:
- The axion quality problem (ensuring PQV operators do not spoil the strong CP solution).
- Current limits on axion isocurvature perturbations from CMB observations.
- The requirement that the axion abundance matches the observed DM density ( $m_a n_a/s \approx 0.22$ eV).
- The requirement that the baryon asymmetry matches the observed value ( $Y_B \approx 0.87 \times 10^{-10}$ ).

Key Contributions

Unified Framework: The paper presents a generic axion-driven cogenesis scenario where both BAU and DM originate from kinetic misalignment, unifying the PQ mechanism with the Type-I seesaw sector.
Mechanism for Rotation: It identifies Hubble-induced masses and higher-dimensional PQ-violating operators as the drivers for early-time axion rotation, decoupling the PQ sector from the specific microphysics of inflation.
Predictive Mass Range: The authors derive a specific relationship linking the right-handed neutrino mass ( $m_N$ ) to the axion decay constant ( $f_a$ ) and the efficiency of the leptogenesis process ( $\kappa$ ).
Robustness: The analysis demonstrates that successful cogenesis is achievable across a broad range of Hubble scales ( $H_0 < H_I$ ) and PQ-breaking scales ( $H_c < f_a$ ), independent of the specific inflationary model details, provided the PQ symmetry is broken during inflation.

Results

Baryon Asymmetry: The kinetic misalignment generates a non-trivial $B-L$ number, leading to a baryon asymmetry $n_B = c_B \dot{\theta} T^2 / 6$ . For the DFSZ model with $N_f=3$ , the coefficient is calculated as $c_B = -2.3$ .
Right-Handed Neutrino Mass: Successful cogenesis predicts a right-handed neutrino mass in the range:
$m_N \approx 3.7 \frac{NDW}{\sqrt{|c_B| \cdot \kappa(K)}} \left(\frac{f_a}{10^9 \text{ GeV}}\right)^{1/2} \text{ TeV}$
For $f_a \in [2.5 \times 10^8, 10^{12}]$ GeV, this corresponds to $m_N$ in the range of $[O(10), O(100)]$ TeV (scaled by $f_a^{1/2}$ ).
Parameter Space: The study delineates allowed regions for the Hubble scale at the end of inflation ( $H_0$ ) and the scale of PQ breaking ( $H_c$ ) for various PQV operator dimensions ( $n$ ) and decay constants ( $f_a$ ). The results show that the model satisfies axion quality constraints and isocurvature limits while maintaining the necessary conditions for cogenesis.
Initial Conditions: The analysis covers both vanishing initial abundance ( $Y_N(0)=0$ ) and thermal initial abundance ( $Y_N(0)=Y_N^{eq}$ ) for the right-handed neutrinos, showing viable solutions for both scenarios.

Significance
The paper establishes kinetic axion misalignment as a "robust and predictive mechanism" for axion cogenesis. Its primary significance lies in demonstrating that the simultaneous generation of baryon asymmetry and dark matter can be achieved without relying on restrictive inflationary models or specific inflaton-PQ couplings. By decoupling inflation from the PQ sector while still utilizing Hubble-induced effects to drive the dynamics, the framework offers a flexible solution that connects the strong CP problem, neutrino physics (via the Type-I seesaw), and the dark sector. The authors claim this provides a consistent link between these fundamental sectors of the universe, remaining viable across a wide range of parameters and satisfying current observational constraints.