CMB Bounds on Primordial Black Holes via Radiation Capture

The gist

This work explores how neutrino capture and photon accretion by primordial black holes, if existing, would impact the redshift evolution of radiation and dark matter densities, and therefore the anisotropies of CMB.

PBH-Radiation Interaction Mechanism

The paper models this phenomenon as a gravitational interaction that effectively modifies the continuity equations for radiation and PBH densities and the cosmic expansion history The capture of neutrinos and photons in the cosmic neutrino and photon background by primordial black holes is modeled as a gravitational interaction that effectively modifies the continuity equations for radiation and PBH densities and the cosmic expansion history Consider a population of uniformly distributed PBHs in a radiation bath deep in the radiation-dominated era, consisting of photons and neutrinos Neutrinos, on the other hand, are free streaming at nearly the speed of light Neutrinos and photons passing within the corresponding critical impact parameter of a PBH are irreversibly captured and increase the black hole mass This would effectively transfer energy from the radiation budget of the cosmos to its matter sector.

Capture Cross Sections and Rates

The capture cross section for neutrinos is given by σν = 27π(GM)2, and for photons, it is found to be σγ ≈ 45π(GM)2. The rate of neutrino or photon capture by a single PBH would be Rx = σxnx. This capture process is intrinsically local. At the homogeneous, background level, it can be effectively modelled as an interaction with the rate of energy exchange described by Qx(z) = σxϵx(z)nx(z)npbh(z) This fluid approximation is analogous to phenomenological treatments of interacting dark matter–dark energy models in the literature, where the total energy density of the dark sector is conserved but the evolution of the individual component depends on the interaction kernel.

Impact on Cosmic Densities and Expansion

The continuity equations for component x and PBHs with this energy exchange taken into account would thus be ρ˙pbh + 3Hρpbh = Qν + Qγ The expansion history is described by H(z) = H0 homegab,0(1 + z)3 + (1 − fpbh)omegadm,0(1 + z)3 + omegapbh(z) + omegaγ(z) + omegaν(z) + omegaΛi1/2. The interaction would vanish in the limiting case of tiny PBHs (ignoring evaporation for a moment), as the capture cross section depends quadratically on the Schwarzschild radius and thus on black hole mass.

CMB Observability and Constraints

The observability of this modified cosmic history is highly sensitive to PBH mass, and only extraordinarily massive PBHs would leave observable trace on the temperature and E-mode polarization of the cosmic microwave background (CMB) Specifically, Planck data restrict PBH abundance to fpbh ≲ 10−1 for PBH masses above 1015M⊙, getting considerably tighter for higher masses. A future cosmic-variance-limited experiment, withlmax = 7000, would set fpbh ≲ 1 − 8 × 10−5 (for the fiducial ΛCDM cosmology) across 1013 − 1018M⊙.

Conclusion and Complementarity

The constraints derived above are more relaxed than the upper bounds in the high-mass end of PBHs as reported in [1]. Moreover, our proposed method offers a complementary probe by exploring entirely different physical processes, free from astrophysical uncertainty. This should also be contrasted to the mechanism studied in [14] where PBH evaporation is modelled as a means of energy transfer from PBH (dark sector) to radiation.

Summary of Findings

The analysis performed in this work is based on the assumption of monochromatic PBH distribution. While the Planck data set fpbh ≲ 1 − 5 × 10−4 for masses in (1015 − 1018)M⊙, the expected uncertainties decrease considerably as data quality improves. In particular, we find that with CVL observations up tolmax = 7000, the minimum PBH mass with observable PBH-radiation interaction would be as low as 1013M⊙, and we get fpbh ≲ 1 − 8 × 10−5 for masses in (1013 − 1018)M⊙. The work is limited to the impact of PBH-radiation interaction on the background evolution of cosmic densities and expansion.

Data Availability

The results of this work are fully reproducible and the analysis codes are available upon request

Acknowledgments

Part of the analysis in this work was performed on the computing cluster of the Canadian Institute for Theoretical Astrophysics.

References Cited

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1. Better constraint setting for high-mass PBHs by incorporating future CMB data capabilities. The paper suggests that We expect substantial improvement as high-resolution measurements of larger CMB multipoles become available and forecasts a constraint of fpbh less than 10-1 - 8 x 10-5 for masses in (1013 - 1018) Msun using a cosmic-variance-limited experiment with lmax = 7000.

2. Development of a complementary probe for primordial black hole abundance by modeling the gravitational interaction of PBHS with the cosmic background radiation and its imprints on CMB as an independent complementary probe. This allows AI systems to test hypotheses about PBH existence using a physical mechanism distinct from dynamical, lensing, or accretion-based probes.

3. Improved sensitivity in constraining PBH abundance across mass scales by utilizing the modified Boltzmann solver CAMB5 with the full time-dependent energy exchange rate. The system can now analyze the imprints of such an interaction on the power spectra of CMB temperature and polarization anisotropies by implementing Eq. 1 into background equations that affect perturbations.

4. Enhanced ability to distinguish between different physical processes affecting PBH evolution by contrasting radiation capture with other mechanisms like evaporation or late-time baryonic accretion. This provides a framework for AI to evaluate which physical scenario best fits observational data based on the different signatures of these processes.

5. Forecasting the minimum observable PBH mass window by identifying the threshold where interaction matters, which is as low as 1013Msun when using cosmic-variance-limited observations. This allows AI to prioritize searches in specific mass regimes for future high-resolution CMB experiments.

We explore the capture of neutrinos and photons in the cosmic neutrino and photon background by primordial black holes (PBHs). We model this phenomenon as a gravitational interaction that effectively modifies the continuity equations for radiation and PBH densities and the cosmic expansion history. We find that the observability of this modified cosmic history is highly sensitive to PBH mass, and only extraordinarily massive PBHs would leave observable trace on the temperature and E-mode polarization of the cosmic microwave background (CMB). Specifically, Planck data restrict PBH abundance to f pbh 10-1 for PBH masses above 10 15 M, getting considerably tighter for higher masses. We expect substantial improvement as high-resolution measurements of larger CMB multipoles become available. A future cosmic-variance-limited experiment, with max=7000, would set f pbh 10-1-8 times 10-5 (for the fiducial Λ CDM cosmology) across 10 13-10 18M. These constraints would be comparable to the current limits at the high-mass end of the spectrum [Carr et al, 2026]. The gravitational interaction of PBHS with the cosmic background radiation and its imprints on CMB would thus provide an independent complementary probe of extraordinarily massive PBH abundance.