- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Probing primordial black hole mergers in clusters with pulsar timing data

Sonali Verma, Virgile Dandoy, and Sébastien Clesse

  • Service de Physique Théorique, Brussels Laboratory of the Universe BLU-ULB, Université Libre de Bruxelles, Boulevard du Triomphe, CP225, 1050 Brussels, Belgium

PDF

Phys. Rev. D 114, 083532 – Published 20 October, 2026

DOI: https://doi.org/10.1103/j38g-ft2h

Abstract

We consider the possibility that the stochastic gravitational wave (GW) background suggested by pulsar timing array (PTA) datasets is sourced by primordial black holes (PBHs). Specifically, we perform a Bayesian search in the International PTA data release 2 (IPTA DR2) for a combined GW background arising from scalar perturbations and unresolved PBH mergers, assuming a broad PBH mass distribution. In our analysis, we incorporate constraints on the curvature power spectrum from cosmic microwave background μ distortions and the overproduction of PBHs, which significantly suppress the contribution of PBH mergers to the total GW background. We find that scalar-induced GWs dominate the nanohertz frequency range, while PBH mergers alone cannot account for the observed signal under the standard PBH formation scenario involving Gaussian perturbations and including only Poissonian PBH clustering. However, specific PBH models, such as those with enhanced clustering, could yield a GW background dominated by PBH mergers. Overall, we find that the IPTA DR2 strongly favors an astrophysical origin for the reported common-spectrum process over the PBH models considered in this analysis.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (150)

  1. Y. B. Zel’dovich and I. D. Novikov, The hypothesis of cores retarded during expansion and the hot cosmological model, Sov. Astron. 10, 602 (1967).
  2. S. W. Hawking, Black hole explosions?, Nature (London) 248, 30 (1974).
  3. G. F. Chapline, Cosmological effects of primordial black holes, Nature (London) 253, 251 (1975).
  4. B. J. Carr, The primordial black hole mass spectrum, Astrophys. J. 201, 1 (1975).
  5. S. M. Leach, M. Sasaki, D. Wands, and A. R. Liddle, Enhancement of superhorizon scale inflationary curvature perturbations, Phys. Rev. D 64, 023512 (2001).
  6. G. Ballesteros and M. Taoso, Primordial black hole dark matter from single field inflation, Phys. Rev. D 97, 023501 (2018).
  7. S. S. Mishra and V. Sahni, Primordial black holes from a tiny bump/dip in the inflaton potential, J. Cosmol. Astropart. Phys. 04 (2019) 007.
  8. J. Liu, L. Bian, R.-G. Cai, Z.-K. Guo, and S.-J. Wang, Primordial black hole production during first-order phase transitions, Phys. Rev. D 105, L021303 (2022).
  9. M. J. Baker, M. Breitbach, J. Kopp, and L. Mittnacht, Primordial black holes from first-order cosmological phase transitions, Phys. Lett. B 868, 139625 (2025).
  10. K. Kawana and K.-P. Xie, Primordial black holes from a cosmic phase transition: The collapse of Fermi-balls, Phys. Lett. B 824, 136791 (2022).
  11. C. Gross, G. Landini, A. Strumia, and D. Teresi, Dark matter as dark dwarfs and other macroscopic objects: Multiverse relics?, J. High Energy Phys. 09 (2021) 033.
  12. J. Garriga, A. Vilenkin, and J. Zhang, Black holes and the multiverse, J. Cosmol. Astropart. Phys. 02 (2015) 064.
  13. B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, Constraints on primordial black holes, Rep. Prog. Phys. 84, 116902 (2021).
  14. S. Chandrasekhar, The maximum mass of ideal white dwarfs, Astrophys. J. 74, 81 (1931).
  15. M. Prunier, G. Morrás, J. F. N. n. Siles, S. Clesse, J. García-Bellido, and E. Ruiz Morales, Analysis of the subsolar-mass black hole candidate SSM200308 from the second part of the third observing run of advanced LIGO-Virgo, Phys. Dark Universe 46, 101582 (2024).
  16. G. Morras et al., Analysis of a subsolar-mass compact binary candidate from the second observing run of Advanced LIGO, Phys. Dark Universe 42, 101285 (2023).
  17. R. Abbott et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Search for subsolar-mass black hole binaries in the second part of Advanced LIGO’s and Advanced Virgo’s third observing run, Mon. Not. R. Astron. Soc. 524, 5984 (2023); 526, 6234(E) (2023).
  18. K. S. Phukon, G. Baltus, S. Caudill, S. Clesse, A. Depasse, M. Fays, H. Fong, S. J. Kapadia, R. Magee, and A. J. Tanasijczuk, The hunt for sub-solar primordial black holes in low mass ratio binaries is open, Phys. Rev. D 114, 063529 (2026).
  19. S. Clesse and J. Garcia-Bellido, GW190425, GW190521 and GW190814: Three candidate mergers of primordial black holes from the QCD epoch, Phys. Dark Universe 38, 101111 (2022).
  20. V. De Luca, V. Desjacques, G. Franciolini, P. Pani, and A. Riotto, GW190521 mass gap event and the primordial black hole scenario, Phys. Rev. Lett. 126, 051101 (2021).
  21. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW190814: Gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object, Astrophys. J. Lett. 896, L44 (2020).
  22. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW190521: A binary black hole merger with a total mass of 150M⊙, Phys. Rev. Lett. 125, 101102 (2020).
  23. E. Bagui et al. (LISA Cosmology Working Group Collaboration), Primordial black holes and their gravitational-wave signatures, Living Rev. Relativity 28, 1 (2025).
  24. S. Pi and M. Sasaki, Gravitational waves induced by scalar perturbations with a lognormal peak, J. Cosmol. Astropart. Phys. 09 (2020) 037.
  25. K. Inomata and T. Terada, Gauge independence of induced gravitational waves, Phys. Rev. D 101, 023523 (2020).
  26. K. Kohri and T. Terada, Semianalytic calculation of gravitational wave spectrum nonlinearly induced from primordial curvature perturbations, Phys. Rev. D 97, 123532 (2018).
  27. G. Agazie et al. (NANOGrav Collaboration), The NANOGrav 15 yr data set: Observations and timing of 68 millisecond pulsars, Astrophys. J. Lett. 951, L9 (2023).
  28. G. Agazie et al. (NANOGrav Collaboration), The NANOGrav 15 yr data set: Evidence for a Gravitational-wave background, Astrophys. J. Lett. 951, L8 (2023).
  29. J. Antoniadis et al. (EPTA, InPTA Collaborations), The second data release from the European pulsar timing array—III. Search for gravitational wave signals, Astron. Astrophys. 678, A50 (2023).
  30. J. Antoniadis et al. (EPTA Collaboration), The second data release from the European pulsar timing array—I. The dataset and timing analysis, Astron. Astrophys. 678, A48 (2023).
  31. D. J. Reardon et al., Search for an isotropic gravitational-wave background with the Parkes pulsar timing array, Astrophys. J. Lett. 951, L6 (2023).
  32. H. Xu et al., Searching for the nano-hertz stochastic gravitational wave background with the Chinese pulsar timing array data release I, Res. Astron. Astrophys. 23, 075024 (2023).
  33. J. Antoniadis et al., The International Pulsar Timing Array second data release: Search for an isotropic gravitational wave background, Mon. Not. R. Astron. Soc. 510, 4873 (2022).
  34. R. W. Hellings and G. S. Downs, Upper limits on the isotropic gravitational radiation background from pulsar timing analysis., Astrophys. J. Lett. 265, L39 (1983).
  35. A. Afzal et al. (NANOGrav Collaboration), The NANOGrav 15 yr data set: Search for signals from new physics, Astrophys. J. Lett. 951, L11 (2023).
  36. J. Ellis, M. Fairbairn, G. Franciolini, G. Hütsi, A. Iovino, M. Lewicki, M. Raidal, J. Urrutia, V. Vaskonen, and H. Veermäe, What is the source of the PTA GW signal?, Phys. Rev. D 109, 023522 (2024).
  37. V. De Luca, G. Franciolini, and A. Riotto, NANOGrav data hints at primordial black holes as dark matter, Phys. Rev. Lett. 126, 041303 (2021).
  38. K. Harigaya, K. Inomata, and T. Terada, Induced gravitational waves with kination era for recent pulsar timing array signals, Phys. Rev. D 108, 123538 (2023).
  39. S. A. Hosseini Mansoori, F. Felegray, A. Talebian, and M. Sami, PBHs and GWs from T2-inflation and NANOGrav 15-year data, J. Cosmol. Astropart. Phys. 08 (2023) 067.
  40. Z. Yi, Z.-Q. You, Y. Wu, Z.-C. Chen, and L. Liu, Exploring the NANOGrav signal and planet-mass primordial black holes through Higgs inflation, J. Cosmol. Astropart. Phys. 06 (2023) 043.
  41. S. Balaji, G. Domènech, and G. Franciolini, Scalar-induced gravitational wave interpretation of PTA data: The role of scalar fluctuation propagation speed, J. Cosmol. Astropart. Phys. 10 (2023) 041.
  42. D. G. Figueroa, M. Pieroni, A. Ricciardone, and P. Simakachorn, Cosmological background interpretation of pulsar timing array data, Phys. Rev. Lett. 132, 171002 (2024).
  43. A. J. Iovino, G. Perna, A. Riotto, and H. Veermäe, Curbing PBHs with PTAs, J. Cosmol. Astropart. Phys. 10 (2024) 050.
  44. M. Braglia, J. Garcia-Bellido, and S. Kuroyanagi, Testing primordial black holes with multi-band observations of the stochastic gravitational wave background, J. Cosmol. Astropart. Phys. 12 (2021) 012,
  45. G. Ferrante, G. Franciolini, A. Iovino, Junior., and A. Urbano, Primordial black holes in the curvaton model: Possible connections to pulsar timing arrays and dark matter, J. Cosmol. Astropart. Phys. 06 (2023) 057.
  46. E. Madge, E. Morgante, C. Puchades-Ibáñez, N. Ramberg, W. Ratzinger, S. Schenk, and P. Schwaller, Primordial gravitational waves in the nano-Hertz regime and PTA data—towards solving the GW inverse problem, J. High Energy Phys. 10 (2023) 171.
  47. K. Inomata, K. Kohri, and T. Terada, Detected stochastic gravitational waves and subsolar-mass primordial black holes, Phys. Rev. D 109, 063506 (2024).
  48. V. Dandoy, V. Domcke, and F. Rompineve, Search for scalar induced gravitational waves in the International Pulsar Timing Array data release 2 and NANOgrav 12.5 years datasets, SciPost Phys. Core 6, 060 (2023).
  49. P. F. Depta, K. Schmidt-Hoberg, P. Schwaller, and C. Tasillo, Do pulsar timing arrays observe merging primordial black holes?, Phys. Rev. Res. 7, 013196 (2025).
  50. Y. Gouttenoire, S. Trifinopoulos, G. Valogiannis, and M. Vanvlasselaer, Scrutinizing the primordial black hole interpretation of PTA gravitational waves and JWST early galaxies, Phys. Rev. D 109, 123002 (2024).
  51. C. T. Byrnes, M. Hindmarsh, S. Young, and M. R. S. Hawkins, Primordial black holes with an accurate QCD equation of state, J. Cosmol. Astropart. Phys. 08 (2018) 041.
  52. A. Moradinezhad Dizgah, G. Franciolini, and A. Riotto, Primordial black holes from broad spectra: Abundance and clustering, J. Cosmol. Astropart. Phys. 11 (2019) 001.
  53. T. D. Brandt, Constraints on MACHO dark matter from compact stellar systems in ultra-faint dwarf galaxies, Astrophys. J. Lett. 824, L31 (2016).
  54. B. Carr, S. Clesse, J. Garcia-Bellido, M. Hawkins, and F. Kuhnel, Observational evidence for primordial black holes: A positivist perspective, Phys. Rep. 1054, 1 (2024).
  55. E. Bagui and S. Clesse, A boosted gravitational wave background for primordial black holes with broad mass distributions and thermal features, Phys. Dark Universe 38, 101115 (2022).
  56. J. Chluba, A. L. Erickcek, and I. Ben-Dayan, Probing the inflaton: Small-scale power spectrum constraints from measurements of the CMB energy spectrum, Astrophys. J. 758, 76 (2012).
  57. B. B. P. Perera et al., The International Pulsar Timing Array: Second data release, Mon. Not. R. Astron. Soc. 490, 4666 (2019).
  58. T. Bringmann, P. F. Depta, V. Domcke, and K. Schmidt-Hoberg, Towards closing the window of primordial black holes as dark matter: The case of large clustering, Phys. Rev. D 99, 063532 (2019).
  59. M. Raidal, V. Vaskonen, and H. Veermäe, Gravitational waves from primordial black hole mergers, J. Cosmol. Astropart. Phys. 09 (2017) 037.
  60. G. Ballesteros, P. D. Serpico, and M. Taoso, On the merger rate of primordial black holes: effects of nearest neighbours distribution and clustering, J. Cosmol. Astropart. Phys. 10 (2018) 043.
  61. S. Young, The primordial black hole formation criterion re-examined: Parametrisation, timing and the choice of window function, Int. J. Mod. Phys. D 29, 2030002 (2019).
  62. B. Carr, S. Clesse, J. García-Bellido, and F. Kühnel, Cosmic conundra explained by thermal history and primordial black holes, Phys. Dark Universe 31, 100755 (2021).
  63. W. H. Press and P. Schechter, Formation of galaxies and clusters of galaxies by selfsimilar gravitational condensation, Astrophys. J. 187, 425 (1974).
  64. A. D. Gow, C. T. Byrnes, P. S. Cole, and S. Young, The power spectrum on small scales: Robust constraints and comparing PBH methodologies, J. Cosmol. Astropart. Phys. 02 (2020) 002.
  65. M. W. Choptuik, Universality and scaling in gravitational collapse of a massless scalar field, Phys. Rev. Lett. 70, 9 (1993).
  66. J. C. Niemeyer and K. Jedamzik, Near-critical gravitational collapse and the initial mass function of primordial black holes, Phys. Rev. Lett. 80, 5481 (1998).
  67. J. C. Niemeyer and K. Jedamzik, Dynamics of primordial black hole formation, Phys. Rev. D 59, 124013 (1999).
  68. S. Young, I. Musco, and C. T. Byrnes, Primordial black hole formation and abundance: Contribution from the non-linear relation between the density and curvature perturbation, J. Cosmol. Astropart. Phys. 11 (2019) 012.
  69. G. Franciolini, I. Musco, P. Pani, and A. Urbano, From inflation to black hole mergers and back again: Gravitational-wave data-driven constraints on inflationary scenarios with a first-principle model of primordial black holes across the QCD epoch, Phys. Rev. D 106, 123526 (2022).
  70. V. Vaskonen and H. Veermäe, Did NANOGrav see a signal from primordial black hole formation?, Phys. Rev. Lett. 126, 051303 (2021).
  71. K. Ando, K. Inomata, and M. Kawasaki, Primordial black holes and uncertainties in the choice of the window function, Phys. Rev. D 97, 103528 (2018).
  72. A. Escrivà, C. Germani, and R. K. Sheth, Universal threshold for primordial black hole formation, Phys. Rev. D 101, 044022 (2020).
  73. I. Musco, Threshold for primordial black holes: Dependence on the shape of the cosmological perturbations, Phys. Rev. D 100, 123524 (2019).
  74. I. Musco, V. De Luca, G. Franciolini, and A. Riotto, Threshold for primordial black holes. II. A simple analytic prescription, Phys. Rev. D 103, 063538 (2021).
  75. A. Escrivà, E. Bagui, and S. Clesse, Simulations of PBH formation at the QCD epoch and comparison with the GWTC-3 catalog, J. Cosmol. Astropart. Phys. 05 (2022) 004.
  76. G. Domènech, Scalar induced gravitational waves review, Universe 7, 398 (2021).
  77. K. N. Ananda, C. Clarkson, and D. Wands, The cosmological gravitational wave background from primordial density perturbations, Phys. Rev. D 75, 123518 (2007).
  78. E. Bugaev and P. Klimai, Induced gravitational wave background and primordial black holes, Phys. Rev. D 81, 023517 (2010).
  79. L. Alabidi, K. Kohri, M. Sasaki, and Y. Sendouda, Observable spectra of induced gravitational waves from inflation, J. Cosmol. Astropart. Phys. 09 (2012) 017.
  80. D. Baumann, P. J. Steinhardt, K. Takahashi, and K. Ichiki, Gravitational wave spectrum induced by primordial scalar perturbations, Phys. Rev. D 76, 084019 (2007).
  81. G. Domènech, S. Pi, A. Wang, and J. Wang, Induced gravitational wave interpretation of PTA data: A complete study for general equation of state, J. Cosmol. Astropart. Phys. 08 (2024) 054.
  82. G. Franciolini, A. Iovino, Junior., V. Vaskonen, and H. Veermae, Recent gravitational wave observation by pulsar timing arrays and primordial black holes: The importance of non-Gaussianities, Phys. Rev. Lett. 131, 201401 (2023).
  83. L. Liu, Z.-C. Chen, and Q.-G. Huang, Implications for the non-Gaussianity of curvature perturbation from pulsar timing arrays, Phys. Rev. D 109, L061301 (2024).
  84. S. Wang, Z.-C. Zhao, J.-P. Li, and Q.-H. Zhu, Implications of pulsar timing array data for scalar-induced gravitational waves and primordial black holes: Primordial non-Gaussianity fNL considered, Phys. Rev. Res. 6, L012060 (2024).
  85. C. Yuan, D.-S. Meng, and Q.-G. Huang, Full analysis of the scalar-induced gravitational waves for the curvature perturbation with local-type non-Gaussianities, J. Cosmol. Astropart. Phys. 12 (2023) 036.
  86. J. R. Espinosa, D. Racco, and A. Riotto, A cosmological signature of the SM Higgs instability: Gravitational waves, J. Cosmol. Astropart. Phys. 09 (2018) 012.
  87. T. Nakamura, M. Sasaki, T. Tanaka, and K. S. Thorne, Gravitational waves from coalescing black hole MACHO binaries, Astrophys. J. Lett. 487, L139 (1997).
  88. K. Ioka, T. Chiba, T. Tanaka, and T. Nakamura, Black hole binary formation in the expanding universe: Three body problem approximation, Phys. Rev. D 58, 063003 (1998).
  89. M. Raidal, C. Spethmann, V. Vaskonen, and H. Veermäe, Formation and evolution of primordial black hole binaries in the early universe, J. Cosmol. Astropart. Phys. 02 (2018) 018.
  90. V. Vaskonen and H. Veermäe, Lower bound on the primordial black hole merger rate, Phys. Rev. D 101, 043015 (2020).
  91. G. Hütsi, M. Raidal, and H. Veermäe, Small-scale structure of primordial black hole dark matter and its implications for accretion, Phys. Rev. D 100, 083016 (2019).
  92. P. Meszaros, Primeval black holes and galaxy formation, Astron. Astrophys. 38, 5 (1975).
  93. D. Inman and Y. Ali-Haïmoud, Early structure formation in primordial black hole cosmologies, Phys. Rev. D 100, 083528 (2019).
  94. M. S. Delos, A. Rantala, S. Young, and F. Schmidt, Structure formation with primordial black holes: Collisional dynamics, binaries, and gravitational waves, J. Cosmol. Astropart. Phys. 12 (2024) 005.
  95. S. Clesse and J. García-Bellido, Seven hints for primordial black hole dark matter, Phys. Dark Universe 22, 137 (2018).
  96. J. C. Mather et al., Measurement of the cosmic microwave background spectrum by the COBE FIRAS instrument, Astrophys. J. 420, 439 (1994).
  97. D. J. Fixsen, E. S. Cheng, J. M. Gales, J. C. Mather, R. A. Shafer, and E. L. Wright, The cosmic microwave background spectrum from the full COBE FIRAS data set, Astrophys. J. 473, 576 (1996).
  98. G. Hütsi, M. Raidal, V. Vaskonen, and H. Veermäe, Two populations of LIGO-Virgo black holes, J. Cosmol. Astropart. Phys. 03 (2020) 068.
  99. S. Biot and S. Clesse (to be published).
  100. K. Kadota and J. Silk, Boosting small-scale structure via primordial black holes and implications for sub-GeV dark matter annihilation, Phys. Rev. D 103, 043530 (2021).
  101. H. Mouri and Y. Taniguchi, Runaway merging of black holes: Analytical constraint on the timescale, Astrophys. J. Lett. 566, L17 (2002).
  102. G. D. Quinlan and S. L. Shapiro, Dynamical evolution of dense clusters of compact stars, Astrophys. J. 343, 725 (1989).
  103. S. Bird, I. Cholis, J. B. Muñoz, Y. Ali-Haïmoud, M. Kamionkowski, E. D. Kovetz, A. Raccanelli, and A. G. Riess, Did LIGO detect dark matter?, Phys. Rev. Lett. 116, 201301 (2016).
  104. J. F. Navarro, C. S. Frenk, and S. D. M. White, The structure of cold dark matter halos, Astrophys. J. 462, 563 (1996).
  105. A. D. Ludlow, S. Bose, R. E. Angulo, L. Wang, W. A. Hellwing, J. F. Navarro, S. Cole, and C. S. Frenk, The mass–concentration–redshift relation of cold and warm dark matter haloes, Mon. Not. R. Astron. Soc. 460, 1214 (2016).
  106. F. Prada, A. A. Klypin, A. J. Cuesta, J. E. Betancort-Rijo, and J. Primack, Halo concentrations in the standard LCDM cosmology, Mon. Not. R. Astron. Soc. 423, 3018 (2012).
  107. Y. Ali-Haïmoud, E. D. Kovetz, and M. Kamionkowski, Merger rate of primordial black-hole binaries, Phys. Rev. D 96, 123523 (2017).
  108. V. De Luca, V. Desjacques, G. Franciolini, and A. Riotto, The clustering evolution of primordial black holes, J. Cosmol. Astropart. Phys. 11 (2020) 028.
  109. E. S. Phinney, A practical theorem on gravitational wave backgrounds, arXiv:astro-ph/0108028.
  110. S. Clesse and J. García-Bellido, Detecting the gravitational wave background from primordial black hole dark matter, Phys. Dark Universe 18, 105 (2017).
  111. V. Mandic, S. Bird, and I. Cholis, Stochastic gravitational-wave background due to primordial binary black hole mergers, Phys. Rev. Lett. 117, 201102 (2016).
  112. X.-J. Zhu, E. Howell, T. Regimbau, D. Blair, and Z.-H. Zhu, Stochastic gravitational wave background from coalescing binary black holes, Astrophys. J. 739, 86 (2011).
  113. A. Mitridate, D. Wright, R. von Eckardstein, T. Schröder, J. Nay, K. Olum, K. Schmitz, and T. Trickle, ptarcade, arXiv:2306.16377.
  114. A. Mitridate, ptarcade 10.5281/zenodo.7876430 (2023).
  115. G. Desvignes et al. (EPTA Collaboration), High-precision timing of 42 millisecond pulsars with the European Pulsar Timing Array, Mon. Not. R. Astron. Soc. 458, 3341 (2016).
  116. Z. Arzoumanian et al. (NANOGrav Collaboration), The NANOGrav nine-year data set: Observations, arrival time measurements, and analysis of 37 millisecond pulsars, Astrophys. J. 813, 65 (2015).
  117. R. N. Manchester et al. (PPTA Collaboration), The Parkes Pulsar Timing Array project, Pub. Astron. Soc. Aust. 30, e017 (2013).
  118. D. J. Reardon et al., Timing analysis for 20 millisecond pulsars in the Parkes Pulsar Timing Array, Mon. Not. R. Astron. Soc. 455, 1751 (2016).
  119. R. A. Allsman et al. (Macho Collaboration), MACHO project limits on black hole dark matter in the 1-30 solar mass range, Astrophys. J. Lett. 550, L169 (2001).
  120. M. Oguri, J. M. Diego, N. Kaiser, P. L. Kelly, and T. Broadhurst, Understanding caustic crossings in giant arcs: Characteristic scales, event rates, and constraints on compact dark matter, Phys. Rev. D 97, 023518 (2018).
  121. P. Mróz et al., No massive black holes in the milky way halo, Nature (London) 632, 749 (2024).
  122. Y. Inoue and A. Kusenko, New x-ray bound on density of primordial black holes, J. Cosmol. Astropart. Phys. 10 (2017) 034.
  123. P. D. Serpico, V. Poulin, D. Inman, and K. Kohri, Cosmic microwave background bounds on primordial black holes including dark matter halo accretion, Phys. Rev. Res. 2, 023204 (2020).
  124. D. Agius, R. Essig, D. Gaggero, F. Scarcella, G. Suczewski, and M. Valli, Feedback in the dark: A critical examination of CMB bounds on primordial black holes, J. Cosmol. Astropart. Phys. 07 (2024) 003.
  125. M. Andrés-Carcasona, A. J. Iovino, V. Vaskonen, H. Veermäe, M. Martínez, O. Pujolàs, and L. M. Mir, Constraints on primordial black holes from LIGO-Virgo-KAGRA O3 events, Phys. Rev. D 110, 023040 (2024).
  126. H. Kawai and M. Oguri, Constraints on primordial black holes from the observed number of Icarus-like ultrahigh magnification events, arXiv:2411.13816.
  127. F. Ziparo, S. Gallerani, A. Ferrara, and F. Vito, Cosmic radiation backgrounds from primordial black holes, Mon. Not. R. Astron. Soc. 517, 1086 (2022).
  128. G. Facchinetti, M. Lucca, and S. Clesse, Relaxing CMB bounds on primordial black holes: The role of ionization fronts, Phys. Rev. D 107, 043537 (2023).
  129. S. M. Koushiappas and A. Loeb, Dynamics of dwarf galaxies disfavor stellar-mass black holes as dark matter, Phys. Rev. Lett. 119, 041102 (2017).
  130. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW170104: Observation of a 50-solar-mass binary black hole coalescence at redshift 0.2, Phys. Rev. Lett. 118, 221101 (2017); 121, 129901(E) (2018).
  131. G. Franciolini, K. Kritos, E. Berti, and J. Silk, Primordial black hole mergers from three-body interactions, Phys. Rev. D 106, 083529 (2022).
  132. I. Cholis, E. D. Kovetz, Y. Ali-Haïmoud, S. Bird, M. Kamionkowski, J. B. Muñoz, and A. Raccanelli, Orbital eccentricities in primordial black hole binaries, Phys. Rev. D 94, 084013 (2016).
  133. G. Franciolini, A. Kehagias, S. Matarrese, and A. Riotto, Primordial black holes from inflation and non-Gaussianity, J. Cosmol. Astropart. Phys. 03 (2018) 016.
  134. V. De Luca, G. Franciolini, and A. Riotto, Constraining the initial primordial black hole clustering with CMB distortion, Phys. Rev. D 104, 063526 (2021).
  135. C. Ünal, E. D. Kovetz, and S. P. Patil, Multimessenger probes of inflationary fluctuations and primordial black holes, Phys. Rev. D 103, 063519 (2021).
  136. Y. Akrami et al. (Planck Collaboration), Planck 2018 results. IX. Constraints on primordial non-Gaussianity, Astron. Astrophys. 641, A9 (2020).
  137. D. Hooper, A. Ireland, G. Krnjaic, and A. Stebbins, Supermassive primordial black holes from inflation, J. Cosmol. Astropart. Phys. 04 (2023) 021.
  138. G. Agazie et al. (NANOGrav Collaboration), The NANOGrav 15 yr data set: Constraints on supermassive black hole binaries from the gravitational-wave background, Astrophys. J. Lett. 952, L37 (2023).
  139. N. Afshordi, P. McDonald, and D. N. Spergel, Primordial black holes as dark matter: The power spectrum and evaporation of early structures, Astrophys. J. Lett. 594, L71 (2003).
  140. R. Murgia, G. Scelfo, M. Viel, and A. Raccanelli, Lyman-α Forest constraints on primordial black holes as dark matter, Phys. Rev. Lett. 123, 071102 (2019).
  141. J.-O. Gong and N. Kitajima, Small-scale structure and 21 cm fluctuations by primordial black holes, J. Cosmol. Astropart. Phys. 08 (2017) 017.
  142. A. Kashlinsky, LIGO gravitational wave detection, primordial black holes and the near-IR cosmic infrared background anisotropies, Astrophys. J. Lett. 823, L25 (2016).
  143. A. M. Green, Microlensing and dynamical constraints on primordial black hole dark matter with an extended mass function, Phys. Rev. D 94, 063530 (2016).
  144. J. D. Simon, The faintest dwarf galaxies, Annu. Rev. Astron. Astrophys. 57, 375 (2019).
  145. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  146. R. Abbott et al. (KAGRA, Virgo, and LIGO Scientific Collaborations), Upper limits on the isotropic gravitational-wave background from Advanced LIGO and Advanced Virgo’s third observing run, Phys. Rev. D 104, 022004 (2021).
  147. S. Mukherjee and J. Silk, Can we distinguish astrophysical from primordial black holes via the stochastic gravitational wave background?, Mon. Not. R. Astron. Soc. 506, 3977 (2021).
  148. S. Mukherjee, M. S. P. Meinema, and J. Silk, Prospects of discovering subsolar primordial black holes using the stochastic gravitational wave background from third-generation detectors, Mon. Not. R. Astron. Soc. 510, 6218 (2022).
  149. J. M. Bardeen, J. R. Bond, N. Kaiser, and A. S. Szalay, The statistics of peaks of Gaussian random fields, Astrophys. J. 304, 15 (1986).
  150. X. Pritchard, C. T. Byrnes, J. Lesgourgues, and D. Sharma, Robust μ-distortion constraints on primordial supermassive black holes from cubic (gNL) non-Gaussian perturbations, J. Cosmol. Astropart. Phys. 07 (2025) 079.

Outline

Information

Phys. Rev. D 114, 083532– Published 20 October, 2026
  • Received 28 October 2025
  • Accepted 28 September 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation