⚛️ high-energy theory

Primordial Black Hole mass growth from neutrinos during radiation era

This paper proposes that primordial black holes can undergo significant mass growth through neutrino absorption during the radiation era, a mechanism that alters their predicted mass distribution, shifts thermal history peaks, and modifies their potential contribution to dark matter.

Original authors: Maël Gonin

Published 2026-07-13

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Maël Gonin

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 early universe as a giant, super-hot soup, churning with energy and particles. For decades, scientists have been trying to figure out what happened to the "baby" black holes (called Primordial Black Holes, or PBHs) born in this soup. The old story was simple: these black holes were too small to eat much, and the soup was too thick for them to swallow anything significant. They were supposed to stay the same size forever.

But this new paper suggests a twist in the tale: some of these baby black holes might have actually gorged themselves on a specific ingredient in the soup—neutrinos—growing into much larger giants than we thought.

The Old Rule vs. The New Idea

For a long time, the scientific community believed that black holes couldn't grow much during the radiation era (the very hot, early phase of the universe). The reasoning was like this: imagine trying to drink a thick milkshake through a tiny straw. The "straw" is the black hole's ability to grab matter, and the "milkshake" is the radiation. Scientists thought the particles in the soup were so crowded that they couldn't get close enough to the black hole to be eaten. They argued that the "mean free path" (how far a particle can travel before bumping into something else) was too short for the black hole to catch them.

This paper doesn't throw that old rule away completely, but it says, "Wait a minute, that rule doesn't apply at every moment." The authors suggest that if you look closely at how these particles move (their "kinetics"), there are times when the soup is just right. Specifically, they propose that neutrinos—ghostly, tiny particles that barely interact with anything—can actually be swallowed by these black holes if the black hole is big enough and the timing is right.

The "Sweet Spot" of Eating

The authors used a semi-classical approach (a mix of quantum rules and classical physics) to simulate this process. They found that while the study considers a broad range of black hole masses from $10^{-3}$ to $10^9$ solar masses ( $M_\odot$ ), only those with masses of at least $10^3$ solar masses significantly absorb neutrinos.

However, not all black holes get a full meal. The paper identifies a "sweet spot" for eating.

The Goldilocks Zone: Black holes with masses around $10^3$ to $10^5$ solar masses ( $M_\odot$ ) seem to be the perfect size. They form at a time when the universe is cooling down just enough for neutrinos to be available but not yet too sparse.
The Timing: It's like a buffet that closes early. The universe is expanding and cooling. If a black hole is born too late (when the universe is cooler), the neutrinos have already "frozen out" or stopped interacting with the soup, so there's nothing left to eat. If it's born too early, the conditions aren't right for the absorption to start.
The Result: In their simulations, these intermediate-sized black holes can grow significantly. The paper notes that for a specific parameter called the "collapse fraction" ( $\gamma$ ) set to 0.55, the mass growth is substantial. If this fraction gets too high (above 0.55), the growth becomes "runaway," meaning the black hole would eat so fast the math breaks down, which suggests nature probably keeps this value in check.

A New Map of the Universe

This eating habit changes the map of the universe. The authors suggest that because these black holes are gaining mass, the distribution of black hole sizes we expect to see today would look different.

Shifting Peaks: The paper predicts that the "peaks" in the number of black holes at certain masses would shift. For example, a peak caused by electron-positron ( $e^+e^-$ ) physics would move to larger masses.
A New Peak: Most excitingly, the absorption process might create a new peak in the middle of the mass spectrum (around $10^3$ to $10^7$ $M_\odot$ ). This would be a cluster of black holes that grew just enough to stand out from the rest.
Dark Matter: Since these black holes are growing, they would make up a larger chunk of the universe's "dark matter" (the invisible stuff holding galaxies together). The paper calculates that the fraction of dark matter in these black holes ( $f_{PBH}$ ) could change depending on how the transition from "not eating" to "eating" happens. For instance, if the transition is sharp, the fraction could be around 0.1260, but if it's smoother, it might drop to 0.1107.

What This Means for Us

The authors are careful to say this is a "new picture" based on their simulations and a closer look at the physics, not a proven fact yet. They acknowledge that they haven't accounted for all the complexities of the early universe, like imbalances between matter and antimatter (lepton asymmetry), which might change the numbers.

However, if this idea holds up, it could solve a mystery. Astronomers have spotted some very bright, early galaxies that seem to have supermassive black holes at their centers. It's been hard to explain how these giants grew so big so fast. This paper suggests that if neutrino absorption is real, these "baby" black holes could have had a massive growth spurt early on, becoming the "little red dots" seen by the James Webb Space Telescope without needing to rely on huge, rare fluctuations in the early universe.

In short, the paper suggests that the early universe wasn't just a place where black holes sat still; for a brief, specific window, some of them might have been busy snacking on neutrinos, growing into the giants we see today. It's a fresh perspective that challenges the old view that black holes in the radiation era were stuck in a food coma.

Technical Summary: Primordial Black Hole Mass Growth from Neutrinos During the Radiation Era

Problem Statement
The prevailing view in cosmology, established by Carr and Hawking (1974), posits that Primordial Black Holes (PBHs) cannot undergo significant mass growth during the radiation-dominated era. This conclusion relies on the argument that the mean free path of radiation ( $\lambda_{rad}^{mfp}$ ) is much smaller than the PBH Schwarzschild radius ( $r_S$ ), preventing efficient hydrodynamical accretion. Consequently, PBHs are generally assumed to retain their initial formation mass. However, this assumption has not been rigorously re-examined through the lens of primordial plasma kinetics, specifically regarding the absorption of neutrino radiation. This paper challenges the static mass assumption by investigating whether PBHs can absorb neutrinos when the condition $\lambda_{rad}^{mfp} > r_S$ is met, potentially altering the PBH mass spectrum and their contribution to Dark Matter (DM).

Methodology
The authors employ a semi-classical approach, treating PBHs as black body radiation absorbers embedded in a thermal bath, rather than relying on hydrodynamical fluid calculations. The study focuses on the kinetic conditions of the early plasma to determine when neutrino absorption becomes possible.

Kinetic Conditions: The authors define a transition temperature, $T_{start}$ , where the neutrino mean free path ( $\lambda_\nu^{mfp}$ ) exceeds the Schwarzschild radius ( $r_S$ ) of the PBH. Below this temperature, absorption is kinematically allowed.
Absorption Modeling: To account for the uncertainty in the transition between non-absorbing and absorbing regimes, the authors introduce a weight function $W = e^{-\kappa r_S/\lambda_\nu^{mfp}}$ , where $\kappa$ represents the path length in units of mean free path.
Mass Evolution Equation: The mass growth is traced by solving an Ordinary Differential Equation (ODE) for the ratio $R = M_{PBH}^{abs}/M_{PBH}^{init}$ $R = M_{P B H}^{ab s} / M_{P B H}^{ini t}$ over the time interval $[T_{start}, T_{eq}]$ $[T_{s t a r t}, T_{e q}]$ (from the onset of absorption to matter-radiation equality). The ODE incorporates:
- The effective collapse fraction $\gamma_{eff}$ , which accounts for the criticality of the collapse.
- The ratio of neutrino energy density to total energy density ( $\delta_{hf}/\alpha$ ).
- The scale factor evolution $x = a/a_{init}$ .
Spectrum Reconstruction: The initial PBH mass spectrum, derived from a Gaussian fluctuation spectrum and Press-Schechter statistics, is updated by multiplying the initial distribution by the growth factor $R(M_{PBH})$ .

Key Contributions

Revisiting Accretion Limits: The paper demonstrates that the Carr and Hawking condition ( $\lambda_{rad}^{mfp} \ll r_S$ ) does not hold at all times. Specifically, for neutrinos, the mean free path becomes larger than the Schwarzschild radius for intermediate and supermassive PBHs, allowing for absorption.
Semi-Classical Framework: The work provides a specific semi-classical framework for calculating PBH mass growth based on neutrino absorption, distinct from geometric cross-section or Stefan-Boltzmann equilibrium approaches used in recent related literature.
Parameter Constraints: The study derives a divergence bound for the collapse fraction $\gamma$ . It identifies that for $\gamma \gtrsim 0.55$ , the absorption process in the "sweet spot" temperature window leads to runaway mass growth, effectively constraining the viable parameter space for PBH formation models.

Results

Mass Growth Regime: Significant mass growth ( $R > 1$ ) occurs primarily for PBHs with masses $M \gtrsim 10^3 M_\odot$ . The growth is most efficient for PBHs formed in the temperature window $T \sim 10 \text{ MeV} - 1 \text{ MeV}$ (post-QCD transition), where neutrinos constitute a dominant fraction of the radiation energy density.
Spectral Features:
- Peak Shift: The absorption mechanism shifts the predicted $e^+e^-$ peak in the PBH mass distribution toward larger masses.
- Additional Peak: An additional peak emerges in the intermediate mass range ( $10^3 - 10^7 M_\odot$ ) corresponding to the "absorption sweet spot" where formation time coincides with the onset of efficient neutrino absorption.
- Dark Matter Fraction: The fraction of Dark Matter in PBHs ( $f_{PBH}$ ) increases due to mass growth. For an initial fraction $f_{PBH}^{init} = 0.1$ , the updated fraction $f_{PBH}^{abs}$ ranges from approximately 0.11 to 0.126 depending on the transition sharpness ( $\kappa$ ) and the collapse fraction ( $\gamma$ ).
Runaway Absorption: The study finds that if $\gamma > 0.55$ , the mass growth diverges for PBHs in the optimal temperature window, suggesting a strict upper limit on $\gamma$ to avoid unphysical runaway scenarios.

Significance and Claims
The paper claims to revise the historical view that PBHs cannot grow in mass during the radiation era. By demonstrating that neutrino absorption is a viable mechanism for mass growth, the authors argue that:

PBHs as Probes: The PBH mass spectrum is a more complex probe of the early Universe's thermal history and plasma kinetics than previously thought, as it is distorted by absorption effects.
Intermediate Mass Seeds: The production of intermediate-mass PBHs ( $10^3 - 10^5 M_\odot$ ) does not rely solely on large initial density fluctuations; they can grow from smaller seeds via neutrino absorption.
Observational Implications: These findings have direct implications for Dark Matter scenarios involving PBHs. Specifically, the rapid growth of light seeds could explain the "little red dots" observed by the James Webb Space Telescope (JWST), as these objects could evade constraints based on primordial fluctuations by growing significantly after formation.

The authors maintain a modest scope, noting that the study treats the PBH spectrum as a "toy model" and does not yet account for lepton or baryon asymmetries, which are deferred to future work. The results are presented as a necessary revision to the understanding of PBH evolution, with specific implications for interpreting observational data and constraining inflation scenarios.

The Old Rule vs. The New Idea

The "Sweet Spot" of Eating

A New Map of the Universe

What This Means for Us

Technical Summary: Primordial Black Hole Mass Growth from Neutrinos During the Radiation Era

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