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Primordial black holes are five dimensional

Luis A. Anchordoqui1,2,3, Alek Bedroya4, and Dieter Lüst5,6

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Phys. Rev. D 114, 063551 – Published 28 September, 2026

DOI: https://doi.org/10.1103/g12h-93th

Abstract

We revisit well-established mechanisms for primordial black hole (PBH) production, namely inflation, phase transitions, and cosmic strings, in the context of the dark dimension scenario, which is motivated by swampland principles. Applying quantum gravity constraints, we demonstrate that any viable mechanism, barring exotic new physics at low energies, inevitably leads to the formation of five-dimensional PBHs. We further show that PBHs formed from cosmic strings can have lifetimes comparable to the age of the Universe. We comment on the observational implications of this result, including a potential connection to the recent detection of a high-energy neutrino by KM3NeT, whose energy is intriguingly close to the five-dimensional Planck scale in the dark dimension scenario.

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References (59)

  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. Hawking, Gravitationally collapsed objects of very low mass, Mon. Not. R. Astron. Soc. 152, 75 (1971).
  3. G. F. Chapline, Cosmological effects of primordial black holes, Nature (London) 253, 251 (1975).
  4. B. Carr and F. Kuhnel, Primordial black holes as dark matter: Recent developments, Annu. Rev. Nucl. Part. Sci. 70, 355 (2020).
  5. N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, The hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429, 263 (1998).
  6. I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, New dimensions at a millimeter to a Fermi and superstrings at a TeV, Phys. Lett. B 436, 257 (1998).
  7. N. B. Agmon, A. Bedroya, M. J. Kang, and C. Vafa, Lectures on the string landscape and the Swampland, arXiv:2212.06187.
  8. D. Lüst, E. Palti, and C. Vafa, AdS and the Swampland, Phys. Lett. B 797, 134867 (2019).
  9. M. Montero, C. Vafa, and I. Valenzuela, The dark dimension and the Swampland, J. High Energy Phys. 02 (2023) 022.
  10. E. Gonzalo, M. Montero, G. Obied, and C. Vafa, Dark dimension gravitons as dark matter, J. High Energy Phys. 11 (2023) 109.
  11. G. Obied, C. Dvorkin, E. Gonzalo, and C. Vafa, Dark dimension and decaying dark matter gravitons, Phys. Rev. D 109, 063540 (2024).
  12. K. R. Dienes and B. Thomas, Dynamical dark matter: I. Theoretical overview, Phys. Rev. D 85, 083523 (2012).
  13. L. A. Anchordoqui, I. Antoniadis, and D. Lüst, Dark dimension, the swampland, and the dark matter fraction composed of primordial black holes, Phys. Rev. D 106, 086001 (2022).
  14. L. A. Anchordoqui, I. Antoniadis, and D. Lüst, Dark dimension, the swampland, and the dark matter fraction composed of primordial near-extremal black holes, Phys. Rev. D 109, 095008 (2024).
  15. L. A. Anchordoqui, I. Antoniadis, and D. Lüst, More on black holes perceiving the dark dimension, Phys. Rev. D 110, 015004 (2024).
  16. A. Bedroya, C. Vafa, and D. H. Wu, The tale of three scales: The Planck, the species, and the black hole scales, arXiv:2403.18005.
  17. R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70, 2837 (1993).
  18. G. T. Horowitz and J. Polchinski, Selfgravitating fundamental strings, Phys. Rev. D 57, 2557 (1998).
  19. B. Balthazar, J. Chu, and D. Kutasov, On small black holes in string theory, J. High Energy Phys. 03 (2024) 116.
  20. A. Bedroya and D. Wu, String stars in d≥7, arXiv:2412.19888.
  21. P. Ivanov, P. Naselsky, and I. Novikov, Inflation and primordial black holes as dark matter, Phys. Rev. D 50, 7173 (1994).
  22. M. Crawford and D. N. Schramm, Spontaneous generation of density perturbations in the early universe, Nature (London) 298, 538 (1982).
  23. S. W. Hawking, Black holes from cosmic strings, Phys. Lett. B 231, 237 (1989).
  24. A. Bedroya and C. Vafa, Trans-Planckian censorship and the Swampland, J. High Energy Phys. 09 (2020) 123.
  25. A. Bedroya, R. Brandenberger, M. Loverde, and C. Vafa, Trans-Planckian censorship and inflationary cosmology, Phys. Rev. D 101, 103502 (2020).
  26. A. Bedroya, Q. Lu, and P. Steinhardt, TCC in the interior of moduli space and its implications for the string landscape and cosmology, arXiv:2407.08793.
  27. N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity, Phys. Rev. D 59, 086004 (1999).
  28. S. Aiello et al. (KM3NeT Collaboration), Observation of an ultra-high-energy cosmic neutrino with KM3NeT, Nature (London) 638, 376 (2025); 640, E3 (2025).
  29. L. A. Anchordoqui, F. Halzen, and D. Lüst, Neutrinos from primordial black holes in theories with extra dimensions, Phys. Rev. D 112, 083034 (2025).
  30. A. Bedroya, H. Lee, and P. Steinhardt, A species scale-driven breakdown of effective field theory in time-dependent string backgrounds, arXiv:2504.13260.
  31. C. Eröncel, Y. Gouttenoire, R. Sato, G. Servant, and P. Simakachorn, Universal bound on the duration of a kination era, Phys. Rev. Lett. 135, 101002 (2025).
  32. L. A. Anchordoqui, A. Bedroya, D. Lüst, and H.-C. Tarazi, IR black hole instabilities trigger species-scale particle production, arXiv:2608.00590.
  33. T. Bhattacharya et al., QCD phase transition with chiral quarks and physical quark masses, Phys. Rev. Lett. 113, 082001 (2014).
  34. C. Schmid, D. J. Schwarz, and P. Widerin, Peaks above the Harrison-Zel’dovich spectrum due to the quark—gluon to hadron transition, Phys. Rev. Lett. 78, 791 (1997).
  35. N. Gendler and C. Vafa, Axions in the dark dimension, J. High Energy Phys. 12 (2024) 127.
  36. M. Kamionkowski and J. March-Russell, Planck scale physics and the Peccei-Quinn mechanism, Phys. Lett. B 282, 137 (1992).
  37. S. M. Barr and D. Seckel, Planck scale corrections to axion models, Phys. Rev. D 46, 539 (1992).
  38. R. Holman, S. D. H. Hsu, T. W. Kephart, E. W. Kolb, R. Watkins, and L. M. Widrow, Solutions to the strong CP problem in a world with gravity, Phys. Lett. B 282, 132 (1992).
  39. S. Ghigna, M. Lusignoli, and M. Roncadelli, Instability of the invisible axion, Phys. Lett. B 283, 278 (1992).
  40. L. Dolan and R. Jackiw, Symmetry behavior at finite temperature, Phys. Rev. D 9, 3320 (1974).
  41. S. Weinberg, Gauge and global symmetries at high temperature, Phys. Rev. D 9, 3357 (1974).
  42. J. E. Kim, Weak interaction singlet and strong CP invariance, Phys. Rev. Lett. 43, 103 (1979).
  43. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Can confinement ensure natural CP invariance of strong interactions?, Nucl. Phys. B166, 493 (1980).
  44. M. Dine, W. Fischler, and M. Srednicki, A simple solution to the strong CP problem with a harmless axion, Phys. Lett. B 104, 199 (1981).
  45. L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli, The landscape of QCD axion models, Phys. Rep. 870, 1 (2020).
  46. S. L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177, 2426 (1969).
  47. J. S. Bell and R. Jackiw, A PCAC puzzle: π0→γγ in the σ model, Nuovo Cimento A 60, 47 (1969).
  48. V. Anastassopoulos et al. (CAST Collaboration), New CAST limit on the axion-photon interaction, Nat. Phys. 13, 584 (2017).
  49. G. G. Raffelt, Astrophysical axion bounds, Lect. Notes Phys. 741, 51 (2008).
  50. I. G. Irastorza and J. Redondo, New experimental approaches in the search for axion-like particles, Prog. Part. Nucl. Phys. 102, 89 (2018).
  51. A. Caputo and G. Raffelt, Astrophysical axion bounds: The 2024 edition, Proc. Sci. COSMICWISPers (2024) 041
  52. P. Svrcek and E. Witten, Axions in string theory, J. High Energy Phys. 06 (2006) 051.
  53. A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell, String axiverse, Phys. Rev. D 81, 123530 (2010).
  54. L. F. T. Airoldi, G. F. S. Alves, Y. F. Perez-Gonzalez, G. M. Salla, and R. Z. Funchal, Could a primordial black hole explosion explain the KM3NeT event?, arXiv:2505.24666.
  55. M. Montero, C. Vafa, and I. Valenzuela, Neutrinos, B-L symmetry and the dark dimension, arXiv:2512.09052.
  56. K. R. Dienes, E. Dudas, and T. Gherghetta, Neutrino oscillations without neutrino masses or heavy mass scales: A higher dimensional seesaw mechanism, Nucl. Phys. B557, 25 (1999).
  57. N. Arkani-Hamed, S. Dimopoulos, G. R. Dvali, and J. March-Russell, Neutrino masses from large extra dimensions, Phys. Rev. D 65, 024032 (2001).
  58. G. R. Dvali and A. Y. Smirnov, Probing large extra dimensions with neutrinos, Nucl. Phys. B563, 63 (1999).
  59. H. Pas, S. Pakvasa, and T. J. Weiler, Sterile-active neutrino oscillations and shortcuts in the extra dimension, Phys. Rev. D 72, 095017 (2005).

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Phys. Rev. D 114, 063551– Published 28 September, 2026
  • Received 15 August 2025
  • Accepted 11 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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