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Primordial black holes through preheating instabilities in α-attractor models

Daniel del-Corral1,2,3,*, Paolo Gondolo4,5,†, K. Sravan Kumar6,‡, and João Marto1,2,§

  • 1Departamento de Física, Universidade da Beira Interior, Rua Marquês D’Ávila e Bolama 6200-001 Covilhã, Portugal
  • 2Centro de Matemática e Aplicações da Universidade da Beira Interior, Rua Marquês D’Ávila e Bolama 6200-001 Covilhã, Portugal
  • 3Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Krakow, Poland
  • 4Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
  • 5Department of Physics, Institute of Science Tokyo, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan
  • 6Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX, United Kingdom

  • *Contact author: daniel.corral.martinez@uj.edu.pl
  • †Contact author: paolo.gondolo@utah.edu
  • ‡Contact author: sravan.kumar@port.ac.uk
  • §Contact author: jmarto@ubi.pt
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Phys. Rev. D 114, 023561 – Published 27 July, 2026

DOI: https://doi.org/10.1103/v9jt-1zpm

Abstract

In this work, we explore the production of primordial black holes (PBHs) within the context of α-attractor inflationary models, focusing on the preheating phase following inflation. During this phase, self-resonance instabilities arise due to deviations of the inflationary potential from a quadratic form. PBH formation is analyzed using three criteria: (i) the perturbation must lie within the instability band, (ii) its characteristic length must exceed the Jeans length, and (iii) it must have sufficient time to collapse based on the estimations of massive scalar field spherical collapse in an Einstein–de Sitter universe. Based on these criteria, we calculate the PBH mass fraction using the altered Press-Schechter (PS) that is generally implemented in preheating scenarios and Khlopov-Polnarev (KP) formalism that considers nonspherical effects. Our results show that the altered PS formalism tends to overestimate PBH abundance during preheating in contrast to the KP formalism. We provide a detailed comparison between these two frameworks with observational constraints from evaporating PBHs. Notably, the altered PS formalism is excluded by these constraints, which are based on Hawking radiation, while the KP formalism remains viable. These findings underscore the importance of accounting for nonspherical effects and accurate collapse dynamics in studies of PBH formation during preheating.

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References (82)

  1. Y. B. Zel’dovich and I. D. Novikov, SOVAST 10, 602 (1967).
  2. S. Hawking, Mon. Not. R. Astron. Soc. 152, 75 (1971).
  3. B. J. Carr and S. W. Hawking, Mon. Not. R. Astron. Soc. 168, 399 (1974).
  4. B. J. Carr, Astrophys. J. 201, 1 (1975).
  5. P. Villanueva-Domingo, O. Mena, and S. Palomares-Ruiz, Front. Astron. Space Sci. 8, 87 (2021).
  6. B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, Rep. Prog. Phys. 84, 116902 (2021).
  7. B. Carr and F. Kuhnel, SciPost Phys. Lect. Notes 48, 1 (2022).
  8. S. W. Hawking, Nature (London) 248, 30 (1974).
  9. D. del Corral, P. Gondolo, K. S. Kumar, and J. Marto, J. Cosmol. Astropart. Phys. 02 (2025) 009.
  10. M. Lemoine, Phys. Lett. B 481, 333 (2000).
  11. T. D. Gomez-Aguilar and L. E. Padilla, pbhbeta: A python package for calculating the abundance of primordial black holes, https://pbhbeta.readthedocs.io/en (2023).
  12. T. D. Gomez-Aguilar and L. E. Padilla, pbhbeta, https://github.com/TadeoDGAguilar/PBHBeta (2023).
  13. J. Martin, T. Papanikolaou, and V. Vennin, J. Cosmol. Astropart. Phys. 01 (2020) 024.
  14. K. Jedamzik, M. Lemoine, and J. Martin, J. Cosmol. Astropart. Phys. 03 (2010) 034.
  15. R. Kallosh and A. Linde, J. Cosmol. Astropart. Phys. 12 (2010) 006.
  16. R. Kallosh and A. Linde, J. Cosmol. Astropart. Phys. 07 (2013) 002.
  17. D. I. Kaiser and E. I. Sfakianakis, Phys. Rev. Lett. 112, 011302 (2014).
  18. R. Kallosh and A. Linde, Phys. Rev. D 91, 083528 (2015).
  19. R. Kallosh, A. Linde, and D. Roest, J. High Energy Phys. 11 (2013) 198.
  20. R. Kallosh and A. Linde, Phys. Rev. D 91, 083528 (2015).
  21. L. Iacconi, M. Fasiello, J. Väliviita, and D. Wands, J. Cosmol. Astropart. Phys. 10 (2023) 015.
  22. J. J. M. Carrasco, R. Kallosh, A. Linde, and D. Roest, Phys. Rev. D 92, 041301 (2015).
  23. K. Alam, M. Bastero-Gil, K. Dutta, and H. V. Ragavendra, J. Cosmol. Astropart. Phys. 11 (2023) 095.
  24. T. Krajewski, K. Turzyński, and M. Wieczorek, Eur. Phys. J. C 79, 654 (2019).
  25. D. del Corral, P. Gondolo, K. S. Kumar, and J. Marto, Phys. Rev. D 113, 023526 (2026).
  26. D. del Corral, Ann. Phys. (Amsterdam) 470, 169824 (2024).
  27. W. H. Press and P. Schechter, Astrophys. J. 187, 425 (1974).
  28. T. Harada, C.-M. Yoo, and K. Kohri, Phys. Rev. D 88, 084051 (2013).
  29. M. Y. Khlopov and A. G. Polnarev, Phys. Lett. 97B, 383 (1980).
  30. A. G. Polnarev and M. Y. Khlopov, Sov. Astron. 25, 406 (1981).
  31. A. G. Polnarev and M. Y. Khlopov, Astron. Zh. 26, 391 (1982).
  32. P. Gondolo, P. Sandick, and B. Shams Es Haghi, Phys. Rev. D 102, 095018 (2020).
  33. Quantum Gravity. Proceedings, 2nd Seminar, Moscow, USSR, October 13–15, 1981, edited by M. A. Markov and P. C. West (Plenum Press, Moscow, 1984).
  34. J. H. MacGibbon, Nature (London) 329, 308 (1987).
  35. S. W. Hawking, Phys. Rev. D 14, 2460 (1976).
  36. P. Chen, Y. C. Ong, and D.-h. Yeom, Phys. Rep. 603, 1 (2015).
  37. Y. Aharonov, A. Casher, and S. Nussinov, Phys. Lett. B 191, 51 (1987).
  38. J. D. Barrow, E. J. Copeland, and A. R. Liddle, Phys. Rev. D 46, 645 (1992).
  39. B. J. Carr, J. H. Gilbert, and J. E. Lidsey, Phys. Rev. D 50, 4853 (1994).
  40. K. S. Kumar and J. Marto, Prog. Theor. Exp. Phys. 2024, 123E01 (2024).
  41. K. S. Kumar and J. Marto, Gen. Relativ. Gravit. 56, 143 (2024).
  42. I. B. Zeldovich, A. A. Starobinskii, M. I. Khlopov, and V. M. Chechetkin, Sov. Astron. Lett. 3, 110 (1977).
  43. S. K. Acharya and R. Khatri, J. Cosmol. Astropart. Phys. 06 (2020) 018.
  44. B. J. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, Phys. Rev. D 81, 104019 (2010).
  45. A. S. Josan, A. M. Green, and K. A. Malik, Phys. Rev. D 79, 103520 (2009).
  46. D. N. Page and S. W. Hawking, Astrophys. J. 206, 1 (1976).
  47. B. Carr and F. Kuhnel, Annu. Rev. Nucl. Part. Sci. 70, 355 (2020).
  48. M. Shafi, E. J. Copeland, R. Mahbub, S. S. Mishra, and S. Basak, J. Cosmol. Astropart. Phys. 10 (2024) 082.
  49. J. C. Niemeyer, Prog. Part. Nucl. Phys. 113, 103787 (2019).
  50. R. R. R. Reis, Phys. Rev. D 67, 087301 (2003); 68, 089901(E) (2003).
  51. J. A. R. Cembranos, A. L. Maroto, and S. J. Núñez Jareño, J. High Energy Phys. 03 (2016) 013.
  52. M. P. Hertzberg, J. Karouby, W. G. Spitzer, J. C. Becerra, and L. Li, Phys. Rev. D 90, 123528 (2014).
  53. A. Escrivà, Universe 8, 66 (2022).
  54. J. Martin, T. Papanikolaou, L. Pinol, and V. Vennin, J. Cosmol. Astropart. Phys. 05 (2020) 003.
  55. S. M. C. V. Goncalves, Phys. Rev. D 62, 124006 (2000).
  56. V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, Phys. Rep. 215, 203 (1992).
  57. D. Baumann, in Theoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small (World Scientific, Boulder, 2011), pp. 523–686.
  58. J. Martin, T. Papanikolaou, L. Pinol, and V. Vennin, J. Cosmol. Astropart. Phys. 05 (2020) 003.
  59. G. Ballesteros, J. Iguaz Juan, P. D. Serpico, and M. Taoso, Phys. Rev. D 111, 083521 (2025).
  60. J. C. Aurrekoetxea, K. Clough, and F. Muia, Phys. Rev. D 108, 023501 (2023).
  61. M. Shibata and M. Sasaki, Phys. Rev. D 60, 084002 (1999).
  62. T. Harada, C.-M. Yoo, T. Nakama, and Y. Koga, Phys. Rev. D 91, 084057 (2015).
  63. T. Harada, C.-M. Yoo, and Y. Koga, Phys. Rev. D 108, 043515 (2023).
  64. I. Musco, Phys. Rev. D 100, 123524 (2019).
  65. A. Escrivà, C. Germani, and R. K. Sheth, Phys. Rev. D 101, 044022 (2020).
  66. T. Harada, H. Iizuka, Y. Koga, and C.-M. Yoo, Phys. Rev. D 111, 023537 (2025).
  67. S. Young, Computation of the abundance of primordial black holes, in Primordial Black Holes, edited by C. Byrnes, G. Franciolini, T. Harada, P. Pani, and M. Sasaki (Springer Nature, Singapore, 2025), pp. 123–153.
  68. A. G. Doroshkevich, Astrophysics (Engl. Transl.) 6, 1573 (1970).
  69. T. Harada, C.-M. Yoo, K. Kohri, K.-i. Nakao, and S. Jhingan, Astrophys. J. 833, 61 (2016).
  70. J. D. Barrow and B. J. Carr, Mon. Not. R. Astron. Soc. 182, 537 (1978).
  71. J. C. Niemeyer and K. Jedamzik, Phys. Rev. Lett. 80, 5481 (1998).
  72. J. C. Niemeyer and K. Jedamzik, Phys. Rev. D 59, 124013 (1999).
  73. A. M. Green and A. R. Liddle, Phys. Rev. D 60, 063509 (1999).
  74. A. D. Gow, C. T. Byrnes, P. S. Cole, and S. Young, J. Cosmol. Astropart. Phys. 02 (2021) 002.
  75. T. Kokubu, K. Kyutoku, K. Kohri, and T. Harada, Phys. Rev. D 98, 123024 (2018).
  76. T. Harada, C.-M. Yoo, K. Kohri, and K.-I. Nakao, Phys. Rev. D 96, 083517 (2017); 99, 069904(E) (2019).
  77. D. Maison, Phys. Lett. B 366, 82 (1996).
  78. J. C. Niemeyer and K. Jedamzik, Phys. Rev. D 59, 124013 (1999).
  79. D. W. Neilsen and M. W. Choptuik, Classical Quantum Gravity 17, 761 (2000).
  80. I. Musco and J. C. Miller, Classical Quantum Gravity 30, 145009 (2013).
  81. M. Snajdr, Classical Quantum Gravity 23, 3333 (2006).
  82. P. J. E. Peebles, The Large-Scale Structure of the Universe (Princeton University Press, Princeton, NJ, 1980).

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Phys. Rev. D 114, 023561– Published 27 July, 2026
  • Received 4 June 2025
  • Accepted 7 July 2026
Article part of CHORUS
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