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Planck isocurvature constraint on primordial black holes lighter than a kiloton

This paper establishes a new upper bound on the abundance of primordial black holes lighter than $10^9$ grams by demonstrating that their biased clustering and non-standard Hawking radiation branching ratios generate isocurvature perturbations constrained by Planck CMB data.

Original authors: TaeHun Kim, Jinn-Ouk Gong, Donghui Jeong, Dong-Won Jung, Yeong Gyun Kim, Kang Young Lee

Published 2026-08-10

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CC BY 4.0

Original authors: TaeHun Kim, Jinn-Ouk Gong, Donghui Jeong, Dong-Won Jung, Yeong Gyun Kim, Kang Young Lee

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 squeezed into a tiny, hot speck. When that speck suddenly inflated, it didn't just get bigger; it got bumpy. These bumps, or "perturbations," are the seeds of everything we see today: stars, galaxies, and the vast empty spaces between them. Usually, scientists think these bumps were perfectly "adiabatic," meaning every type of energy (like light, matter, and dark matter) rose and fell together in perfect harmony, like a choir singing the same note. But what if some of these bumps were "isocurvature"? That's a fancy way of saying the different parts of the universe got out of sync—maybe the light got louder while the matter got quieter, or vice versa.

For decades, we've been hunting for these out-of-sync moments. If we find them, it tells us something wild happened in the very first split second of the universe. One of the most exciting suspects for causing these glitches is the "Primordial Black Hole" (PBH). Think of these not as the giant black holes at the centers of galaxies, but as tiny, microscopic monsters that formed right after the Big Bang. If they were light enough, they wouldn't last forever; they would slowly evaporate, popping out of existence by spitting out particles in a process called Hawking radiation. The big question has always been: if these tiny black holes existed and then vanished, did they leave behind a messy, out-of-sync universe?

This paper, titled "Planck isocurvature constraint on primordial black holes lighter than a kiloton," dives into the mystery of the lightest of these PBHs—ones so small (less than $10^9$ grams, which is about the weight of a large asteroid or a small mountain) that they would have completely evaporated before the universe even started cooking its first atoms (a time called Big Bang Nucleosynthesis). Because they vanished so early, we couldn't see them with our usual telescopes, leaving a huge gap in our knowledge. The authors, a team of physicists from Korea and the US, realized that even though these black holes are gone, they might have left a fingerprint on the Cosmic Microwave Background (CMB)—the afterglow of the Big Bang.

Here is the clever trick the paper uses: When a PBH evaporates, it doesn't just vanish; it shoots out a spray of particles. But here's the catch: the spray isn't always a perfect mix. Sometimes it shoots out more dark matter than light, or more light than dark matter, depending on the black hole's mass and how it formed. Furthermore, these black holes might have formed in "clumps" rather than being spread out evenly. If a clump of black holes evaporates in one spot, it dumps a weird, unbalanced amount of energy there, creating a local "isocurvature" glitch.

The paper calculates that if these light PBHs were common, this glitch would be visible today in the temperature maps of the CMB, specifically in the data collected by the Planck satellite. The authors found that the universe looks too "clean" and too perfectly balanced for these light PBHs to be everywhere. By using the Planck data, they set a new, very strict rule: if these tiny black holes existed, they couldn't have made up more than a tiny, tiny fraction of the early universe's energy.

The study suggests that for certain scenarios (specifically involving a type of cosmic randomness called "non-Gaussianity" with a value around $|f_{NL}| = 0.01$ ), the abundance of these light PBHs is heavily restricted. The paper doesn't say they definitely didn't exist, but it draws a very tight line around how many could have been there. If they were too common, the universe would have looked "messy" in a way that the Planck satellite simply didn't see.

Interestingly, the paper also notes that if these black holes were heavy enough to dominate the universe before they evaporated, the rules change, and the constraints disappear because the universe would have reset itself. But for the vast majority of light PBHs, this new method acts like a cosmic sieve, filtering out the possibility that they were a major player in the early universe. This is a big deal because it's the first time we've been able to put a limit on these specific, super-light black holes that vanished before the first atoms formed. It closes a door on a mass range that was previously a "no-man's-land" for astronomers, showing us that the early universe was likely much more orderly than we might have hoped for these tiny, ghostly monsters.

Technical Summary: Planck Isocurvature Constraint on Primordial Black Holes Lighter than a Kiloton

Problem Statement
Primordial Black Holes (PBHs) with masses $M_{\text{PBH}} \lesssim 10^{15}$ g are expected to have completely evaporated via Hawking radiation before the present epoch. While constraints exist for heavier PBHs ( $10^{17} \text{ g} \lesssim M_{\text{PBH}} \lesssim 10^{22}$ g) that survive to the present day based on gravitational microlensing, gravitational waves, and astrophysical dynamics, and for evaporating PBHs in the range $10^9 \text{ g} \lesssim M_{\text{PBH}} \lesssim 10^{17}$ g based on Cosmic Microwave Background (CMB) distortions, $\gamma$ -rays, and Big Bang Nucleosynthesis (BBN) abundances, a significant gap remains for ultra-light PBHs ( $M_{\text{PBH}} \lesssim 10^9$ g). These lighter PBHs evaporate well before BBN, rendering them invisible to standard BBN constraints and direct observational limits. Consequently, the abundance of PBHs in the mass range $1 \text{ g} \lesssim M_{\text{PBH}} \lesssim 10^9$ g has remained unconstrained.

Methodology
The authors derive new constraints on the abundance of these light PBHs by analyzing the isocurvature perturbations they induce in the CMB. The methodology relies on two primary physical mechanisms that break the adiabatic condition of the early Universe:

Biased Clustering: PBHs form in rare regions with exceptionally large primordial perturbations, making them "biased" tracers of the underlying density field. Consequently, the curvature perturbation associated with PBHs ( $\zeta_{\text{PBH}}$ ) differs from the adiabatic curvature perturbation ( $\zeta$ ) of the background fluid. This bias is modeled using the framework of effective field theory (EFT) and specifically illustrated using local-type primordial non-Gaussianity ( $f_{\text{NL}}$ ), where the PBH number density depends on the long-wavelength modes of the curvature perturbation.
Differential Branching Ratios: The composition of Hawking radiation emitted by evaporating PBHs is determined by the effective Hawking degrees of freedom, which generally differs from the relic abundance ratio of Standard Model particles and Dark Matter (DM).

The authors calculate the final curvature perturbation for each component (photons, baryons, and DM) as a weighted sum of the initial inflationary perturbation and the perturbation induced by PBH evaporation. The resulting isocurvature perturbation between components $X$ and $Y$ is given by:
$S_{XY,0} = 3 \left( \frac{\bar{\rho}_{X\text{PBH},0}}{\bar{\rho}_{X,0}} - \frac{\bar{\rho}_{Y\text{PBH},0}}{\bar{\rho}_{Y,0}} \right) (\zeta_{\text{PBH}} - \zeta)$
where $\bar{\rho}_{X\text{PBH},0}$ represents the energy density contribution from PBH evaporation today.

The analysis assumes a monochromatic PBH mass function and considers a stable scalar DM candidate. The authors compute the energy density fractions of photons and DM produced by evaporation as a function of PBH mass ( $M_{\text{PBH}}$ ) and initial energy fraction ( $\beta$ ). These calculated isocurvature modes are then compared against the upper bounds on non-adiabatic perturbations reported by the Planck 2018 collaboration ( $\beta_{\text{iso}} < 0.001$ ).

Key Contributions and Results

New Constraint Regime: The paper establishes the first observational constraints on PBHs with $M_{\text{PBH}} \lesssim 10^9$ g. By leveraging CMB isocurvature limits, the authors derive upper bounds on the initial energy fraction $\beta(M_{\text{PBH}})$ for PBHs that evaporate before BBN.
Dependence on Dark Matter Mass: The constraints are shown to be highly sensitive to the mass of the Dark Matter particle ( $m_d$ $m_{d}$ ).
- For light DM ( $m_d \lesssim 10^{-5}$ GeV), the isocurvature perturbation is driven primarily by the excess photons from evaporation, leading to constraints that follow the evolution of the PBH energy fraction.
- For heavier DM ( $m_d \gtrsim 10^{-5}$ GeV), the constraints are most stringent when the PBH evaporation temperature matches the DM mass ( $T_{\text{PBH}} \sim m_d$ ), maximizing the DM production from PBHs.
Role of Non-Gaussianity: The derived bounds depend on the assumption of primordial non-Gaussianity (specifically $f_{\text{NL}}$ ), which drives the PBH bias. The paper presents constraints for $|f_{\text{NL}}| = 0.01$ and $|f_{\text{NL}}| = 0.1$ . For $|f_{\text{NL}}| \sim 10^{-2}$ , the constraints are very stringent, limiting the PBH energy fraction to values around $f_{\text{PBH}} \sim \mathcal{O}(0.1)$ at their most restrictive points.
Early Matter Domination: The analysis identifies a regime where PBHs dominate the energy density before evaporating. In this scenario, PBHs become the primary source of cosmological perturbations, causing $\zeta_{\text{PBH}}$ to behave as an adiabatic mode, which suppresses isocurvature modes and relaxes the constraints.

Significance
The paper claims that this work provides the first constraints on the abundance of PBHs lighter than a kiloton ( $10^9$ g), a regime previously unconstrained by direct observation. By linking the small-scale primordial power spectrum (responsible for PBH formation) to CMB isocurvature limits, the study imposes new limits on the amplitude of primordial perturbations at scales much smaller than those probed by standard CMB anisotropy measurements. This offers a potential window into the physics of the post-inflationary Universe, including the end of inflation and the onset of reheating.

Furthermore, the authors note that while their constraints assume complete evaporation, the mechanism relies on Hawking radiation emission. They discuss that scenarios involving stable remnants (e.g., due to the memory burden effect) would also involve Hawking radiation emission prior to stabilization, suggesting that similar observational constraints might apply. However, the authors explicitly state that modifying their constraints to account for such stable relics is beyond the scope of this work and is left for future study.

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