⚛️ high-energy experiments

Dark Transport Erases Baryon Inhomogeneity from Supercooled Phase Transitions

This paper demonstrates that darkogenesis scenarios, where a dark-sector particle transports asymmetry over large distances before decaying into visible baryons, naturally resolve the problem of baryon inhomogeneity induced by supercooled phase transitions, thereby avoiding stringent constraints from Big Bang Nucleosynthesis.

Original authors: Sudhakantha Girmohanta, Kohei Kamada, Yuichiro Nakai, Fumio Uchida

Published 2026-09-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sudhakantha Girmohanta, Kohei Kamada, Yuichiro Nakai, Fumio Uchida

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 story of our universe begins with a profound imbalance. For every particle of matter, there should have been a corresponding particle of antimatter, and they should have annihilated each other in a flash of light, leaving nothing behind. Yet, we exist. The cosmos is filled with stars, planets, and people, all made of matter. This means that in the first moments after the Big Bang, a tiny surplus of matter survived the great annihilation. Physicists call this the baryon asymmetry. To explain how this surplus formed, scientists look to the early universe, a time when the cosmos was a seething, hot soup of particles. They suspect that as the universe cooled, it underwent a dramatic shift, much like water freezing into ice. This shift, known as a phase transition, could have been violent and uneven, creating bubbles of the new, cooler state that expanded and collided. These events are thought to be the very mechanism that tipped the scales, creating the extra matter we see today.

However, this violent birth of matter comes with a serious problem. If the universe cooled down very slowly and suddenly, a process called supercooling, the bubbles of new matter would have formed in a chaotic, patchy way. Imagine a field where some patches freeze first and others later; the result is a landscape of uneven density. In the early universe, this would mean that the amount of matter created in one spot could be vastly different from the amount in a neighboring spot. This unevenness is a disaster for the next chapter of cosmic history: the formation of the first atomic nuclei. A few minutes after the Big Bang, the universe was hot enough to fuse protons and neutrons into light elements like deuterium. The amount of deuterium created depends extremely sensitively on how many protons and neutrons are present in any given region. If the universe were patchy, with some areas rich in matter and others poor, the final mix of elements would be a chaotic mess that does not match the precise, uniform amounts we observe in the sky today. For decades, this conflict has threatened to rule out the very idea that a violent, bubble-driven phase transition created our matter.

A team of researchers has now found a way to resolve this tension, suggesting that the solution lies in a hidden sector of the universe. They propose that the unevenness created by the bubble collisions does not immediately affect the visible matter we see. Instead, the initial imbalance is stored in a type of invisible particle that belongs to a "dark sector," a realm of particles that interact very weakly with the ordinary world. These invisible particles, which the researchers call dark matter candidates, are born with the uneven distribution. But unlike ordinary matter, which is stuck in place and moves very slowly, these dark particles can travel vast distances. They zip through the early universe, carrying their imbalance with them, effectively smoothing out the rough patches long before they ever interact with ordinary protons and neutrons.

The researchers showed that if these dark particles live for a specific amount of time—roughly one-tenth of a second—they have plenty of time to travel and mix the universe's contents. During this brief window, they act like a cosmic blender, erasing the dangerous clumps of matter. Only after this smoothing process is complete do these dark particles decay, transferring their asymmetry to the visible baryons. By the time the visible matter receives the imbalance, the universe is already uniform. The dangerous patches have been washed away, leaving a smooth, even distribution that allows the first atomic nuclei to form exactly as we observe them today. This mechanism works even if the phase transition happened at a relatively low energy level, a scenario that was previously thought to be impossible due to the unevenness problem.

The study also explored how this smoothing happens in detail. They found that the dark particles can move in two different ways depending on how often they bump into other particles. Sometimes they move like a gas, bouncing around and diffusing slowly; other times, they fly freely without hitting anything, streaming across the cosmos. In both cases, the result is the same: the unevenness is erased. The researchers calculated the specific conditions required for this to work, such as how heavy the dark particles must be and how long they must survive. They found that for a universe that reheats to a temperature of about one billion degrees, and for dark particles that live for 0.1 seconds, there is a wide range of possible interactions that successfully erase the inhomogeneity. This means the idea is not just a theoretical possibility but a robust solution that fits within the known laws of physics.

This discovery is particularly important because it opens the door to a specific type of cosmic event that has recently captured the attention of astronomers. Observations of pulsars have hinted at a background hum of gravitational waves, ripples in spacetime that could have been generated by a phase transition at just the right energy scale. If this hum is indeed from such an event, the universe must have been supercooled, and the unevenness problem would have been severe. The new work suggests that the dark sector transport mechanism is the key that unlocks this scenario, allowing the violent bubble collisions to create the gravitational waves and the matter we see, without destroying the delicate balance of light elements. It turns a potential contradiction into a consistent story, where the invisible particles of the dark sector act as the silent guardians of cosmic order, ensuring that the universe is smooth enough to support the complex chemistry of life.

Technical Summary: Dark Transport Erases Baryon Inhomogeneity from Supercooled Phase Transitions

Problem Statement
The paper addresses a critical cosmological tension arising from strongly supercooled first-order phase transitions (PTs) occurring below the TeV scale. While such transitions are attractive sources of stochastic gravitational waves (GWs)—potentially explaining recent nano-hertz signals from pulsar timing arrays (PTA)—they inherently generate large spatial inhomogeneities in the baryon asymmetry. This occurs because the PT proceeds via the nucleation, expansion, and collision of bubbles, imprinting spatial variations on the scale of the mean bubble separation ( $R_*$ ).

For high-scale transitions, ordinary baryon diffusion efficiently smooths these fluctuations before Big Bang Nucleosynthesis (BBN). However, at lower temperatures (GeV scale), the diffusion of protons and neutrons is too slow to erase these inhomogeneities before BBN. Since primordial light-element abundances (specifically deuterium, D/H) depend non-linearly on the local baryon-to-photon ratio ( $\eta$ ), even moderate fluctuations ( $\delta\eta/\eta \sim \mathcal{O}(10\%)$ ) are strongly constrained by observational data. Consequently, standard baryogenesis scenarios tied to low-scale supercooled PTs face stringent constraints or are ruled out by the requirement of a homogeneous baryon distribution at BBN.

Methodology
The authors propose a "darkogenesis" framework where the baryon asymmetry is not generated directly in the Standard Model (SM) sector during the PT. Instead, the PT first generates an asymmetry in a dark-sector (DS) Dirac fermion, $\chi$ . This asymmetry is stored in the DS for a finite period before being transferred to visible baryons via a "neutron portal" interaction (a dimension-6 operator connecting $\chi$ to SM quarks).

The core methodology involves analyzing the transport of the $\chi$ particle, which, being an SM singlet, can travel significantly larger distances than ordinary baryons before decaying. The authors investigate two transport regimes based on the interaction strength of $\chi$ with the thermal plasma:

Diffusive Regime: Where $\chi$ undergoes frequent collisions with thermal particles, leading to a random walk.
Collisionless (Free-streaming) Regime: Where $\chi$ decouples early and travels ballistically, with erasure driven by velocity dispersion.

The authors derive analytic conditions for the "erasure length" ( $L_{erase}$ ) in both regimes, requiring that the distance $\chi$ travels before decaying exceeds the initial inhomogeneity scale ( $R_*$ ). They parameterize the DS interactions via a thermally averaged scattering cross-section, $\langle \sigma v_{rel} \rangle_\chi$ , or an equivalent mass scale $M$ .

To validate their analytic estimates, the authors perform a detailed numerical evaluation. They solve the Boltzmann equations for the $\chi$ phase-space distribution and the subsequent evolution of the SM baryon distribution, accounting for the continuous decay of $\chi$ into neutrons and the subsequent diffusion of SM baryons. This allows them to compare the analytic "sudden-decay" approximation with a more realistic continuous decay scenario.

Key Contributions and Results

Mechanism for Erasure: The paper demonstrates that dark-sector transport can naturally erase baryon inhomogeneities. Because $\chi$ interacts weakly with the thermal plasma, its transport scale is determined by its own diffusion or free-streaming length, which can be orders of magnitude larger than the diffusion length of protons or neutrons.
Analytic Constraints:
- In the diffusive regime, the authors derive a lower bound on the interaction scale $M$ (or an upper bound on the cross-section $\langle \sigma v_{rel} \rangle_\chi$ ) required to ensure $L_{erase}(\tau_\chi) \gtrsim R_*$ . For a representative scenario with a reheating temperature $T_{RH} \sim 1$ GeV, $\beta/H \simeq 10$ , and a $\chi$ lifetime $\tau_\chi \sim 0.1$ s, they find that efficient erasure occurs for $M \gtrsim 65$ TeV (corresponding to $\langle \sigma v_{rel} \rangle_\chi \lesssim 0.8$ pb).
- In the collisionless regime, erasure is governed by the velocity dispersion of $\chi$ . The condition is easily satisfied provided $\tau_\chi \gg t_{RH}$ and $\chi$ possesses a non-zero velocity dispersion (e.g., thermalized shortly after reheating).
Numerical Validation: The numerical analysis reveals that while the dark-sector inhomogeneity is damped exponentially (Gaussian), the resulting baryon inhomogeneity is suppressed as a power law ( $k^{-4/3}$ in the diffusive regime) due to the accumulation of baryons produced by $\chi$ decays at earlier times. Despite this difference, the analytic estimate of the erasure length remains a robust predictor of the damping scale, agreeing with numerical results within an $\mathcal{O}(1)$ factor for initial inhomogeneities of order unity.
Model Example: The authors construct a concrete model where $\chi$ scatters via a Yukawa interaction with a light dark scalar. They show that a coupling $|Y_\chi| \lesssim 10^{-2}$ satisfies the erasure conditions while remaining consistent with constraints from nucleon decays and collider searches.

Significance and Claims
The paper claims to provide a consistent framework for low-scale supercooled phase transitions that generate observable gravitational waves without violating BBN constraints.

Resolution of Tension: It resolves the conflict between the need for strong supercooling (to generate GWs) and the requirement for baryon homogeneity. The authors argue that baryogenesis before the PT is challenged by both the dilution of the pre-existing asymmetry and the imprinting of new inhomogeneities.
Darkogenesis Preference: The work points toward darkogenesis associated with the phase transition as a viable alternative. In this scenario, the asymmetry is generated in the dark sector during the PT and transferred to the visible sector after the inhomogeneities have been efficiently erased by dark transport.
Robustness: The authors emphasize that this mechanism works for a viable range of dark-sector interactions. They note that while the power-law suppression in the baryon sector is less efficient than the Gaussian suppression in the dark sector, it is sufficient to erase inhomogeneities for initial amplitudes of order unity. For models with extremely large initial inhomogeneities, a more detailed, model-dependent treatment would be required.

In conclusion, the paper establishes that dark-sector transport offers a natural solution to the baryon-inhomogeneity problem, making darkogenesis a particularly well-motivated scenario for explaining low-scale supercooled phase transitions, such as those potentially responsible for the PTA GW signal.

Technical Summary: Dark Transport Erases Baryon Inhomogeneity from Supercooled Phase Transitions

More like this