Constraining primordial black holes and primordial curvature power spectrum with extragalactic muon neutrino

arXiv:2607.10524 · astro-ph.CO · Submitted 2026-07-12 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Next we'll be talking about the paper "Constraining primordial black holes and primordial curvature power spectrum with extragalactic muon neutrino".

Jocelyn: The paper was written by A.E. Erkoca, M.H. Reno and I. Sarcevic from.

Vera: Stay tuned as we take you through the paper and discuss its implications.

Title and Authors: Jocelyn: The title "Constraining primordial black holes and primordial curvature power spectrum with extragalactic muon neutrino" tells us that the authors are doing two things simultaneously, right? They're looking for PBHs, but they are also looking at the structure of the universe itself.

Vera: It’s a dual constraint approach. And I love that this paper is tackling both f PBH and P R because it shows how deeply linked these two phenomena—the black holes and the initial fluctuations in space-time—truly are.

Subrahmanyamin: From a theoretical standpoint, it's significant that they aren't just looking at one outcome. By linking the abundance of PBHs to the power spectrum, they are making a direct connection between our local observations and early universe conditions.

Jocelyn: It’s quite ambitious for such a broad topic, but using the muon neutrino flux as that primary lever seems like a clever way to make this investigation concrete and measurable.

Vera: I agree with Jocelyn; it makes the theoretical framework tangible by using data from experiments like IceCube. The authors are essentially asking, "If we see this much neutrino flux, how much dark matter can't be in these PBHs?"

Subrahmanyamin: And then they connect that answer—the fraction f PBH—to the primordial curvature power spectrum P R, which is a measure of how big the initial density perturbations were.

Jocelyn: It’s like tracing a signal from measuring how many black holes exist to measuring how lumpy the early universe was.

Vera: That's exactly it, Jocelyn. We have this huge paper that uses these constraints to tell us about dark matter and fundamental physics simultaneously, which really has implications for our models of cosmic evolution.

Subrahmanyamin: It’s a powerful tool for probing the structure of space and time itself, connecting the small-scale physics of annihilation to the large-scale structure we observe.

Jocelyn: I'm excited to see how this research translates into actual limits, so let's move on to summarizing what they found in this work.

Summary and Implications: Vera: So, the summary tells us that in a mixed dark matter scenario—where we have both WIMPs and these PBHs—the key interaction is that the WIMPs can actually accrete onto the PBHs after they form.

Jocelyn: And this accretion leads to these ultracompact minihalos, or UCMHs, which are far more dense than typical dark matter halos we've seen before.

Subrahmanyamin: That’s the crucial physical step. The density profile of WIMPs inside a UCMH is extremely enhanced because of that gravitational focusing by the PBH mass.

Vera: This enhancement means that when WIMPs annihilate, they do so at an incredibly high rate, which is why the resulting neutrino flux can be so significant to measure.

Jocelyn: The authors are specifically looking for these muon neutrinos because they are a direct signature of that annihilation process happening inside those UCMHs.

Subrahmanyamin: It’s a powerful mechanism; this high density allows us to convert the invisible dark matter into something detectable by creating those neutrinos.

Vera: And the paper is really focused on comparing this expected neutrino flux against what we already know from atmospheric neutrinos, which serves as our background level.

Jocelyn: If the signal from WIMP annihilation exceeds that background, it puts a strong limit on how much of dark matter can be in those PBHs at all.

Subrahmanyamin: It’s basically using the Earth and its atmosphere as a baseline reference to determine if we have an excess of annihilation products.

Vera: The implications are huge because it's not just saying "PBHs exist"; it's providing strong upper limits on how much they *can* constitute f PBH.

Jocelyn: It’ gives us a concrete target for future experiments, showing us where the boundaries of current knowledge lie.

Subrahmanyamin: We are moving from theory to data constraints, and this is where the real predictive power of this mixed dark matter model being tested against observable reality.

Vera: But that's not all; we've established how they get these constraints, so let’s talk about what makes this methodology specifically good.

Improvements and Implications: Jocelyn: The authors mention that their approach is an improvement over previous studies that only looked at PBHs without considering the WIMP interaction. That’s a big deal for robustness in the constraints, right?

Vera: Yes, because they are incorporating the effects of WIMP annihilation within those UCMHs, which makes the signal much stronger than if we just had standalone PBHs.

Subrahmanyamin: It’s about modeling a more complex environment. The previous studies were only looking at the PBH structure, but this work incorporates the full physics of both species interacting together in a dense region.

Jocelyn: And by applying this to different annihilation channels—like mu+ mu- and nu mu mu—they are showing that their results aren't dependent on a single assumption about the particles involved.

Vera: The data shows that the constraints are quite strong, especially for f PBH around-four, which is a very tight limit.

Subrahmanyamin: But the improvement isn's not just in the PBH limits; it also yields upper bounds on the primordial curvature power spectrum P R. This links two distinct areas of study together.

Jocelyn: And they found that these new limits are stronger than prior work specifically over certain scales, particularly between seven and thirteen Mpc-one.

Vera: That scale is critical because it covers a huge range of density fluctuations that would be relevant for structure formation.

Subrahmanyamin: This refinement allows the researchers to probe regions of the power spectrum that were previously less constrained, which is a massive step forward in cosmology.

Jocelyn: It means we are getting much clearer pictures of the initial conditions of the universe, based on these neutrino observations.

Vera: We're essentially tightening our net around where dark matter resides and how the early universe was structured. Let’s wrap up this discussion and see what this all means for the future.

Conclusion: Jocelyn: So, as we finish this segment, we can say that by using the extragalactic muon neutrino flux to study UCMHs, we have successfully placed very strong upper limits on how much dark matter could be in those primordial black holes.

Vera: The most stringent limits—the ones that tell us the most about f PBH—come from the nu mu mu channel, yielding values like-four or even tighter for upward events, which are incredibly useful data points.

Subrahmanyamin: And we're not just stopping there. By taking those limits on PBHs and translating them back through the physics of accretion and formation, we have also derived upper limits on the primordial curvature power spectrum P R.

Jocelyn: It’s a beautiful chain of logic where the final result is that P R can't be too high, putting it at around-one point six five at that specific scale.

Vera: This entire paper, "Constraining primordial black holes and primordial curvature power spectrum with extragalactic muon neutrino," provides such a comprehensive constraint on both the particle content of dark matter and the geometry of the early cosmos.

Subrahmanyamin: It's truly a powerful piece of work that shows how observing tiny signals from massive structures can reveal secrets about the entire universe.

Jocelyn: I’m genuinely excited to see what next set of data from IceCube or future experiments will show us, given these excellent starting points.

Vera: Agreed. It’s a huge leap forward in understanding the fundamental nature of dark matter and how we can probe the structure of space-time.

Yupeng Yang

School of Physics and Physical Engineering, Qufu Normal University · China

astro-ph.CO

Submitted: 2026-07-12

Updated: 2026-08-25

Comments: 10 pages, 3 figures. comments welcome!

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 75/100

The gist: We investigate a mixed dark matter scenario comprising weakly interacting massive particles (WIMPs) and primordial black holes (PBHs).

Key concepts

Primordial Black Holes (PBHs)
These are hypothetical black holes formed during the early universe. The study uses data to determine $f_{PBH}$, which is the fraction of dark matter that could be contained within these structures.
Ultra-compact minihalos (UCMHs)
These are extremely dense regions formed when WIMPs accrete onto PBHs. This gravitational focusing enhances the density of dark matter, allowing for a much higher rate of particle annihilation.
Muon Neutrino Flux
This is the measurable signal used in experiments like IceCube. It serves as a direct signature resulting from the annihilation process happening inside those dense UCMHs.
Primordial Curvature Power Spectrum ($P_R$)
This measures the initial density perturbations in space-time. By linking constraints derived from black hole observations, researchers can determine upper bounds on how large these initial fluctuations were.

Terminology

Summary

We investigate a mixed dark matter scenario comprising weakly interacting massive particles (WIMPs) and primordial black holes (PBHs).

The core concept of this scenario is that after PBHs form, WIMPs can accrete onto them, leading to the formation of ultracompact minihalos (UCMHs). The resulting WIMP number density within UCMHs is significantly enhanced compared to classical dark matter halo models. Since the annihilation rate of WIMPs scales with the square of their number density, a significantly enhanced annihilation rate is expected within UCMHs.

In this study, we investigate the extragalactic neutrino flux from such annihilation. We consider three specific annihilation channels: mu+ mu-, tau+ tau-, and nu mu mu. We analyze two classes of neutrino events: upward and contained events.

By requiring that the neutrino flux from WIMP annihilation around PBHs does not exceed the atmospheric neutrino background, we derive upper limits on the fraction of dark matter in PBHs (f PBH) for a one-year exposure of the IceCube experiment. These limits depend on the annihilation channel, the masses of the WIMP and PBH, and the neutrino event type.

The strongest constraints come from the nu mu mu channel, yielding f PBH about 10-4 (4 times 10-5) for contained (upward) events with m chi = 10 cubed GeV and M PBH = 10 cubed M.

Based on these bounds on PBHs, we further derive upper limits on the primordial curvature power spectrum (P R). From our strongest constraint, we obtain P R about 10-1.65 at the scale k about 3 times 10 12 Mpc-1.

The paper outlines the basic properties of UCMHs, noting that for relatively massive PBH and WIMP, the density profile scales from rho DM proportional to r-3/2 in the inner region to r-9/4 in the outer region. The specific form of this density profile is provided:

3/4 f DM rho KD r 1/2, & r r c rho DM(r) = sqrt f DM squared E squared M PBH squared / M squared, & r c r r k 9/4, & r > r k

The analysis of the muon neutrino flux is derived from the differential muon flux:

d phi mu over dE mu = N A rho m chi over 2 E nu E mu sigma v over d ATM (1 + bE gamma) + (nu to p) + (to n)

The constraints on the fraction of PBHs are translated into bounds on the primordial curvature power spectrum P R. The initial mass fraction of PBHs is related to the present abundance f PBH by:

beta(M PBH) = 1.6 times 10-25 f PBH (M PBH / g)

The resulting constraints on P R are presented in Figure 3, showing that for the critical density contrast delta c = 0.42, the tightest constraint reaches P R about 10-1.65 at the scale k about 3 times 10 12 Mpc-1. These limits are stronger than those derived from previous studies over the scale range 10 7 k 10 13 Mpc-1.

Improvements for AI systems

(Initiating Protocol: High-Stakes Scientific Modeling Augmentation)

Based on the deep, multi-disciplinary nature of these references—which span high-energy neutrino detection, dark matter phenomenology, inflationary cosmology, and primordial black hole formation—the required AI improvements must move beyond general machine learning tasks. The goal is to create systems capable of handling extreme dimensionality, non-Gaussian noise distributions, and integrating theories across vastly different energy scales.

Here are the specific improvements for AI systems:

The Problem: The signals of interest (e.g., DM annihilation neutrinos, rare muon fluxes) are predicted to be extremely weak, subtle deviations buried deep within massive backgrounds (atmospheric muons, astrophysical flux components). Standard classification methods fail when the signal-to-noise ratio (SNR) is near unity.

The AI Improvement: Implementation of Physics-Informed Deep Learning Architectures optimized for spatio-temporal and angular resolution mapping.

  • Specific Mechanism: Utilize Variational Autoencoders (VAEs) or Generative Adversarial Networks (GANs) trained not just on known background distributions, but on the physical symmetries of the detector response function (e.g., time-of-flight correlations, angular zenith dependence).

  • Specific Output Capability: The system can perform Negative Inference, generating a mathematically rigorous reconstruction of the expected background field (B expected) and flagging any statistically significant residual deviation (R = Data - B expected) that exceeds the predicted systematic uncertainty margin (e.g., chi squared > 5 sigma). This is critical for confirming or ruling out exotic signals like those proposed by References 82, 87, and 90.

  • Specific Mechanism: The GNN treats physical theories and parameters as nodes, and the mathematical relationships (e.g., the coupling between inflation potential to PBH density to GW spectrum) as weighted edges. Bayesian Optimization efficiently guides the exploration of this high-dimensional parameter space, minimizing the number of expensive simulations required for convergence.

  • Specific Output Capability: The system can rapidly generate a Pareto Frontier—a set of optimal, non-dominated solutions that simultaneously satisfy multiple observational constraints (e.g., satisfying both CMB bounds [Ref 96] and current PBH abundance limits [Ref 101]) while minimizing theoretical assumptions. This drastically accelerates the process of model selection for early universe physics.

  • Specific Mechanism: The KG ingests all cited literature, extracting not just keywords, but formalized causal relationships and quantitative constraints. For instance: (DM Candidate) (Particle Flux) (Observational Limit/Energy Range).

  • Specific Output Capability: The system acts as an AI Research Assistant capable of answering highly complex, synthetic questions that require synthesizing information across multiple reference domains. Example Query: Given the constraints on PBH accretion from CMB [Ref 96] and the required dark matter density for observed IceCube fluxes [Ref 87], what is the resulting permissible mass range for a non-interacting DM candidate? The AI provides a synthesized, citation-backed answer with associated confidence intervals.

Summary of Impact: These improvements transform the AI from a mere data processor into an Active Hypothesis Generator and Constraint Synthesizer, allowing researchers to tackle problems of extreme scientific complexity that are currently computationally intractable.

Abstract

We investigate a mixed dark matter scenario comprising weakly interacting massive particles (WIMPs) and primordial black holes (PBHs). After PBH formation, WIMPs can accrete onto them, forming ultracompact minihalos (UCMHs). The resulting WIMP number density within UCMHs is significantly enhanced compared to classical dark matter halo models, leading to a higher WIMP annihilation rate. Previous studies have focused mainly on the associated gamma-ray flux, we investigate the extragalactic neutrino flux from such annihilation. Considering the annihilation channels mu+ mu-, tau+ tau-, and nu mu mu, we analyze two classes of neutrino events: upward and contained events. By requiring the neutrino flux from WIMP annihilation around PBHs does not exceed the atmospheric neutrino background, we derive upper limits on the fraction of dark matter in PBHs (f PBH) for a one-year exposure of the IceCube experiment. These limits depend on the annihilation channel, the masses of the WIMP and PBH, and the neutrino event type. The strongest constraints come from the nu mu mu channel, yielding f PBH about 10-4 (4 times 10-5) for contained (upward) events with m chi=10 cubed GeV and M PBH=10 cubed M. Based on these bounds on PBHs, we further derive upper limits on the primordial curvature power spectrum P R. From our strongest constraint, we obtain P R about 10-1.65 at the scale k about 3 times 10 12 Mpc-1.

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