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arxiv: 2606.05133 · v1 · pith:B4LJVJUGnew · submitted 2026-06-03 · 🌌 astro-ph.CO

CMB Bounds on Primordial Black Holes via Radiation Capture

Marzieh Farhang , S. M. S. Movahed This is my paper

Pith reviewed 2026-06-28 04:52 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords primordial black holesCMB constraintsradiation capturecosmic expansion historyPlanck dataPBH abundanceneutrino backgroundphoton background
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The pith

Primordial black holes capture cosmic radiation and modify the expansion history, allowing Planck to bound their abundance below 0.1 for masses above 10^15 solar masses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models the gravitational capture of photons and neutrinos from cosmic backgrounds by primordial black holes as an interaction that changes the continuity equations for radiation and PBH densities. This alteration shifts the cosmic expansion rate in a manner that depends on PBH mass. The modified expansion imprints on the temperature and E-mode polarization of the cosmic microwave background. Planck data then limits the PBH abundance fraction to less than or equal to 0.1 for masses exceeding 10^15 solar masses, with the upper limit becoming substantially lower at higher masses. A future cosmic-variance-limited CMB experiment reaching multipoles up to 7000 is projected to tighten the bound to between 0.1 and 8 times 10 to the minus 5 across the mass range from 10^13 to 10^18 solar masses.

Core claim

The gravitational capture of neutrinos and photons by primordial black holes modifies the continuity equations for radiation and PBH densities and the cosmic expansion history. The observability of this modified history is highly sensitive to PBH mass, and only extraordinarily massive PBHs leave an observable trace on CMB temperature and E-mode polarization. Planck data restrict PBH abundance to f_pbh less than or equal to 0.1 for masses above 10^15 solar masses, with the bound getting considerably tighter for higher masses. A future cosmic-variance-limited experiment with l_max equal to 7000 would set f_pbh less than or equal to 0.1 down to 8 times 10 to the minus 5 across 10^13 to 10^18 so

What carries the argument

Gravitational capture of background photons and neutrinos, modeled through modifications to the continuity equations for radiation and PBH densities that alter the cosmic expansion history.

If this is right

  • Only extraordinarily massive PBHs produce observable effects on CMB temperature and E-mode polarization.
  • Planck data set an upper limit of 0.1 on PBH abundance above 10^15 solar masses, tightening at higher masses.
  • A cosmic-variance-limited experiment to l_max of 7000 constrains abundance from 0.1 down to 8 times 10 to the minus 5 over 10^13 to 10^18 solar masses.
  • The resulting bounds are comparable to existing limits at the high-mass end of the PBH spectrum.
  • The radiation-capture process supplies an independent probe of PBH abundance through its effect on cosmic expansion.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Higher-multipole CMB data could extend constraints to somewhat lower PBH masses than those reachable with current observations.
  • The mass-dependent sensitivity implies that any detected signal would point to a narrow range of very heavy PBHs rather than a broad distribution.
  • If the modeled capture rate holds, the bounds would reduce the allowed contribution of these massive objects to the total energy density at late times.

Load-bearing premise

The capture of radiation by PBHs can be represented entirely as a gravitational process that modifies only the continuity equations and expansion history.

What would settle it

A high-resolution measurement of CMB temperature or E-mode polarization spectra at multipoles above 2000 that matches standard Lambda CDM predictions without any excess power or shift attributable to modified expansion from PBH capture in the 10^13 to 10^18 solar mass range.

Figures

Figures reproduced from arXiv: 2606.05133 by Marzieh Farhang, S. M. S. Movahed.

Figure 1
Figure 1. Figure 1: FIG. 1. Top: Relative change in comoving radiation den [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. PBH mass evolution due to radiation capture for two [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Sensitivity of CMB temperature and E-mode po [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

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 $f_{\rm pbh}\lesssim 10^{-1}$ for PBH masses above $10^{15} M_\odot$, 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 $\ell_{\rm max}=7000$, would set $f_{\rm pbh}\lesssim 10^{-1}-8\times 10^{-5}$ (for the fiducial $\Lambda$CDM cosmology) across $10^{13}-10^{18}M_\odot$. 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper models the gravitational capture of cosmic neutrinos and photons by primordial black holes (PBHs) as an effective interaction that modifies the continuity equations for radiation and PBH energy densities together with the cosmic expansion history. It reports that this effect is observable in the CMB temperature and E-mode polarization only for extraordinarily massive PBHs (M ≳ 10^15 M_⊙), derives Planck-based upper limits f_pbh ≲ 10^{-1} that tighten at higher masses, and forecasts stronger constraints from future high-ℓ CMB data up to ℓ_max = 7000.

Significance. If the effective modification to the continuity equations is shown to be a faithful representation of the underlying microphysics, the work supplies an independent CMB probe of the high-mass tail of the PBH mass function that is complementary to existing limits. The projected sensitivity of a cosmic-variance-limited experiment is stated to reach levels comparable to current high-mass bounds.

major comments (1)
  1. [Abstract / modeling description] The central quantitative bounds rest on the modeling choice that radiation capture can be captured by an effective source term in the continuity equations for ρ_rad and ρ_pbh. No derivation of this effective term, no explicit form of the modified Friedmann or continuity equations, and no numerical implementation or validation against the full Boltzmann hierarchy are provided in the manuscript, making it impossible to assess whether the claimed sensitivity to M > 10^15 M_⊙ is robust or an artifact of the approximation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying the need for greater transparency in the modeling. We address the major comment below and will revise the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [Abstract / modeling description] The central quantitative bounds rest on the modeling choice that radiation capture can be captured by an effective source term in the continuity equations for ρ_rad and ρ_pbh. No derivation of this effective term, no explicit form of the modified Friedmann or continuity equations, and no numerical implementation or validation against the full Boltzmann hierarchy are provided in the manuscript, making it impossible to assess whether the claimed sensitivity to M > 10^15 M_⊙ is robust or an artifact of the approximation.

    Authors: We agree that the current manuscript introduces the effective source term without providing a derivation from the underlying capture physics, the explicit modified equations, or details of the numerical implementation and its relation to the Boltzmann hierarchy. In the revised manuscript we will add a dedicated section that (i) derives the effective source term from the gravitational capture rate of photons and neutrinos by PBHs, (ii) writes out the modified continuity and Friedmann equations in full, (iii) describes the numerical implementation, and (iv) discusses the regime of validity of the effective description together with any comparison to the full hierarchy that is feasible. These additions will allow an independent assessment of whether the reported sensitivity to M ≳ 10^15 M_⊙ is robust. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces a modeling assumption (capture as effective modification to continuity equations) and derives CMB signatures that are then compared directly to external Planck data for bounds on f_pbh. No self-definitional reductions, no parameters fitted to a subset and relabeled as predictions, and no load-bearing self-citations appear in the provided text. The central constraints rest on independent observational input rather than internal re-derivation or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is limited to statements explicitly present there. The central modeling step is treated as a domain assumption rather than derived from first principles.

axioms (1)
  • domain assumption Gravitational interaction of PBHs with cosmic background radiation modifies the continuity equations for radiation and PBH densities and the cosmic expansion history
    Explicitly stated in the abstract as the modeling foundation for the modified cosmic history.

pith-pipeline@v0.9.1-grok · 5781 in / 1229 out tokens · 45451 ms · 2026-06-28T04:52:10.077868+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

40 extracted references · 1 canonical work pages

  1. [1]

    We therefore getσ γ ≈45π(GM) 2

    Using Michel model for the spherical accretion of relativistic fluids, the capture cross section is found to beσ γ = 4πλGR(GM)2c−3 ∞ wherec ∞ is the dimensionless sound speed at infinity andλ GR ≈ 0.7 for a radiation-dominated fluid with adiabatic index Γ = 4/3 [22, 23]. We therefore getσ γ ≈45π(GM) 2. The rate of neutrino or photon capture by a single PB...

    2000

  2. [2]

    B. Carr, A. J. Iovino, G. Perna, V. Vaskonen, and H. Veerm¨ ae, Primordial black holes: constraints, poten- tial evidence and prospects, Nuovo Cimento Rivista Se- rie 10.1007/s40766-026-00080-z (2026), arXiv:2601.06024 [astro-ph.CO]

    work page doi:10.1007/s40766-026-00080-z 2026

  3. [3]

    A. S. Josan, A. M. Green, and K. A. Malik, Gener- alised constraints on the curvature perturbation from pri- mordial black holes, Phys. Rev. D79, 103520 (2009), arXiv:0903.3184 [astro-ph.CO]

    Pith/arXiv arXiv 2009

  4. [4]

    B. J. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, New cosmological constraints on primordial black holes, Phys. Rev. D81, 104019 (2010)

    2010

  5. [5]

    B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, Con- straints on primordial black holes, Rept. Prog. Phys.84, 116902 (2021)

    2021

  6. [6]

    Bellomo, J

    N. Bellomo, J. L. Bernal, A. Raccanelli, and L. Verde, Primordial Black Holes as Dark Matter: Converting Con- straints from Monochromatic to Extended Mass Distri- butions, JCAP01, 004, arXiv:1709.07467 [astro-ph.CO]

    Pith/arXiv arXiv

  7. [7]

    B. Carr, M. Raidal, T. Tenkanen, V. Vaskonen, and H. Veerm¨ ae, Primordial black hole constraints for ex- tended mass functions, Phys. Rev. D96, 023514 (2017), arXiv:1705.05567 [astro-ph.CO]

    Pith/arXiv arXiv 2017

  8. [8]

    Sasaki, T

    M. Sasaki, T. Suyama, T. Tanaka, and S. Yokoyama, Pri- mordial black holes—perspectives in gravitational wave astronomy, Class. Quant. Grav.35, 063001 (2018)

    2018

  9. [9]

    B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, Con- straints on primordial black holes, Rept. Prog. Phys.84, 116902 (2021), arXiv:2002.12778 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  10. [10]

    Carr and F

    B. Carr and F. Kuhnel, Primordial Black Holes as Dark Matter: Recent Developments, Ann. Rev. Nucl. Part. Sci. 70, 355 (2020), arXiv:2006.02838 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  11. [11]

    A. M. Green and B. J. Kavanagh, Primordial Black Holes as a dark matter candidate, J. Phys. G48, 043001 (2021), arXiv:2007.10722 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  12. [12]

    J. R. Rice and B. Zhang, Cosmological evolution of primordial black holes, JHEAp13-14, 22 (2017), arXiv:1702.08069 [astro-ph.HE]. 6

    arXiv 2017

  13. [13]

    De Luca, G

    V. De Luca, G. Franciolini, P. Pani, and A. Riotto, The evolution of primordial black holes and their final ob- servable spins, JCAP04, 052, arXiv:2003.02778 [astro- ph.CO]

    arXiv 2003

  14. [14]

    M. R. Mosbech and Z. S. C. Picker, Effects of Hawking evaporation on PBH distributions, SciPost Phys.13, 100 (2022), arXiv:2203.05743 [astro-ph.HE]

    arXiv 2022

  15. [15]

    Nesseris, D

    S. Nesseris, D. Sapone, and S. Sypsas, Evaporating primordial black holes as varying dark energy, Phys. Dark Univ.27, 100413 (2020), arXiv:1907.05608 [astro- ph.CO]

    arXiv 2020

  16. [16]

    Masina, Dark matter and dark radiation from evap- orating primordial black holes, Eur

    I. Masina, Dark matter and dark radiation from evap- orating primordial black holes, Eur. Phys. J. Plus135, 552 (2020), arXiv:2004.04740 [hep-ph]

    arXiv 2020

  17. [17]

    P. S. Custodio and J. E. Horvath, The Evolution of pri- mordial black hole masses in the radiation dominated era, Gen. Rel. Grav.34, 1895 (2002), arXiv:gr-qc/0203031

    Pith/arXiv arXiv 2002

  18. [18]

    S. Safi, M. Farhang, O. Mena, and E. Di Valentino, Semi- blind reconstruction of the history of effective number of neutrinos using CMB data, Phys. Rev. D110, 103513 (2024), arXiv:2404.01457 [astro-ph.CO]

    arXiv 2024

  19. [19]

    Planck Collaboration, Planck 2018 results. VI. Cosmo- logical parameters (Corrigendum), Astronomy and As- trophysics652, C4 (2021)

    2018

  20. [20]

    J. M. Bardeen, Timelike and null geodesics in the Kerr metric, Proceedings, Ecole d’Et´ e de Physique Th´ eorique: Les Astres Occlus : Les Houches, France, August, 1972, 215-240 , 215 (1973)

    1972

  21. [21]

    C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravi- tation(W. H. Freeman, San Francisco, 1973)

    1973

  22. [22]

    A. F. Zakharov, Capture of photons and slow uncharged particles by a spherically symmetric charged compact body in the relativistic theory of gravitation, Theoret- ical and Mathematical Physics90, 97 (1992)

    1992

  23. [23]

    F. C. Michel, Accretion of Matter by Condensed Objects, Astrophysics and Space Science15, 153 (1972)

    1972

  24. [24]

    Aguayo-Ortiz, E

    A. Aguayo-Ortiz, E. Tejeda, O. Sarbach, and D. L´ opez- C´ amara, Spherical accretion: Bondi, Michel, and rotat- ing black holes, Mon. Not. Roy. Astron. Soc.504, 5039 (2021), arXiv:2102.12529 [astro-ph.HE]

    arXiv 2021

  25. [25]

    Amendola, Coupled quintessence, Phys

    L. Amendola, Coupled quintessence, Phys. Rev. D62, 043511 (2000), arXiv:astro-ph/9908023

    Pith/arXiv arXiv 2000

  26. [26]

    Valiviita, E

    J. Valiviita, E. Majerotto, and R. Maartens, Instability in interacting dark energy and dark matter fluids, JCAP 07, 020, arXiv:0804.0232 [astro-ph]

    Pith/arXiv arXiv

  27. [27]

    Y. L. Bolotin, A. Kostenko, O. A. Lemets, and D. A. Yerokhin, Cosmological Evolution With Interaction Be- tween Dark Energy And Dark Matter, Int. J. Mod. Phys. D24, 1530007 (2014), arXiv:1310.0085 [astro-ph.CO]

    Pith/arXiv arXiv 2014

  28. [28]

    B. Wang, E. Abdalla, F. Atrio-Barandela, and D. Pavon, Dark Matter and Dark Energy Interactions: Theoreti- cal Challenges, Cosmological Implications and Observa- tional Signatures, Rept. Prog. Phys.79, 096901 (2016), arXiv:1603.08299 [astro-ph.CO]

    Pith/arXiv arXiv 2016

  29. [29]

    M. W. Choptuik, Universality and scaling in gravita- tional collapse of a massless scalar field, Phys. Rev. Lett. 70, 9 (1993)

    1993

  30. [30]

    C. R. Evans and J. S. Coleman, Observation of criti- cal phenomena and selfsimilarity in the gravitational col- lapse of radiation fluid, Phys. Rev. Lett.72, 1782 (1994), arXiv:gr-qc/9402041

    Pith/arXiv arXiv 1994

  31. [31]

    J. C. Niemeyer and K. Jedamzik, Near-critical gravi- tational collapse and the initial mass function of pri- mordial black holes, Phys. Rev. Lett.80, 5481 (1998), arXiv:astro-ph/9709072

    Pith/arXiv arXiv 1998

  32. [32]

    B. Carr, F. Kuhnel, and L. Visinelli, Constraints on Stu- pendously Large Black Holes, Mon. Not. Roy. Astron. Soc.501, 2029 (2021), arXiv:2008.08077 [astro-ph.CO]

    arXiv 2029

  33. [33]

    Lewis, A

    A. Lewis, A. Challinor, and A. Lasenby, Efficient com- putation of CMB anisotropies in closed FRW models, Astrophys. J.538, 473 (2000), arXiv:astro-ph/9911177

    Pith/arXiv arXiv 2000

  34. [34]

    Lewis and S

    A. Lewis and S. Bridle, Cosmological parameters from CMB and other data: A Monte Carlo approach, Phys. Rev. D66, 103511 (2002), arXiv:astro-ph/0205436

    Pith/arXiv arXiv 2002

  35. [35]

    Planck Collaboration, Planck 2018 results. X. Con- straints on inflation, Astronomy and Astrophysics641, A10 (2020), arXiv:1807.06211 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  36. [36]

    Beutler, C

    F. Beutler, C. Blake, M. Colless, D. H. Jones, L. Staveley- Smith, L. Campbell, Q. Parker, W. Saunders, and F. Watson, The 6dF Galaxy Survey: Baryon Acous- tic Oscillations and the Local Hubble Constant, Mon. Not. Roy. Astron. Soc.416, 3017 (2011), arXiv:1106.3366 [astro-ph.CO]

    Pith/arXiv arXiv 2011

  37. [37]

    A. J. Ross, L. Samushia, C. Howlett, W. J. Percival, A. Burden, and M. Manera, The clustering of the SDSS DR7 main Galaxy sample – I. A 4 per cent distance mea- sure atz= 0.15, Mon. Not. Roy. Astron. Soc.449, 835 (2015), arXiv:1409.3242 [astro-ph.CO]

    Pith/arXiv arXiv 2015

  38. [38]

    Alamet al.(BOSS), The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sam- ple, Mon

    S. Alamet al.(BOSS), The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sam- ple, Mon. Not. Roy. Astron. Soc.470, 2617 (2017), arXiv:1607.03155 [astro-ph.CO]

    Pith/arXiv arXiv 2017

  39. [39]

    Chen, Q.-G

    L. Chen, Q.-G. Huang, and K. Wang, Constraint on the abundance of primordial black holes in dark mat- ter from Planck data, JCAP12, 044, arXiv:1608.02174 [astro-ph.CO]

    Pith/arXiv arXiv

  40. [40]

    Ali-Ha¨ ımoud and M

    Y. Ali-Ha¨ ımoud and M. Kamionkowski, Cosmic mi- crowave background limits on accreting primordial black holes, Phys. Rev. D95, 043534 (2017), arXiv:1612.05644 [astro-ph.CO]

    Pith/arXiv arXiv 2017