Skip to main content
SpringerLink
Log in

Reconstruction of power spectrum of primordial curvature perturbations on small scales from primordial black hole binaries scenario of LIGO/VIRGO detection

  • Article
  • Editor’s Focus
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

As a candidate bound for the Binary Black Hole (BBH) merger events detected by LIGO/Virgo, Primordial Black Holes (PBHs) provide a useful tool to investigate the primordial curvature perturbations on small scales. Using the GWTC-1 to GWTC-3 catalogs, under the scenario that PBHs originate from large primordial curvature perturbations on small scales during inflationary epoch, we for the first time reconstruct the power spectrum of primordial curvature perturbations on small scales. It is found that the value of the amplitude of the primordial power spectrum is enhanced to \({\cal O}\left({{{10}^{- 2}}} \right)\) on scales \({\cal O}\left(1 \right)\,{\rm{pc}}\). This may imply the validity of PBH as a possible BBH merger candidate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 116, 061102 (2016), arXiv: 1602.03837.

    Article  ADS  MathSciNet  Google Scholar 

  2. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 116, 241103 (2016), arXiv: 1606.04855.

    Article  ADS  Google Scholar 

  3. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. X 8, 039903 (2018).

    Google Scholar 

  4. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 121, 129901 (2018).

    Article  ADS  Google Scholar 

  5. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 119, 141101 (2017), arXiv: 1709.09660.

    Article  ADS  Google Scholar 

  6. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaborations), Astrophys. J. 851, L35 (2017), arXiv: 1711.05578.

    Article  ADS  Google Scholar 

  7. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. X 9, 031040 (2019), arXiv: 1811.12907.

    Google Scholar 

  8. T. Venumadhav, B. Zackay, J. Roulet, L. Dai, and M. Zaldarriaga, Phys. Rev. D 101, 083030 (2020), arXiv: 1904.07214.

    Article  ADS  Google Scholar 

  9. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. X 11, 031040 (2021), arXiv: 2010.14527.

    Google Scholar 

  10. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaborations), arXiv: 2108.01045.

  11. R. Abbott, et al. (The LIGO Scientific Collaboration, the Virgo Collaboration, the KAGRA Collaboration), arXiv: 2111.03606.

  12. K. Belczynski, M. Dominik, T. Bulik, R. OShaughnessy, C. Fryer, and D. E. Holz, Astrophys. J. 715, L138 (2010), arXiv: 1004.0386.

    Article  ADS  Google Scholar 

  13. M. Dominik, K. Belczynski, C. Fryer, D. E. Holz, E. Berti, T. Bulik, I. Mandel, and R. O’Shaughnessy, Astrophys. J. 759, 52 (2012), arXiv: 1202.4901.

    Article  ADS  Google Scholar 

  14. M. Dominik, K. Belczynski, C. Fryer, D. E. Holz, E. Berti, T. Bulik, I. Mandel, and R. O’Shaughnessy, Astrophys. J. 779, 72 (2013), arXiv: 1308.1546.

    Article  ADS  Google Scholar 

  15. M. Dominik, E. Berti, R. OShaughnessy, I. Mandel, K. Belczynski, C. Fryer, D. E. Holz, T. Bulik, and F. Pannarale, Astrophys. J. 806, 263 (2015), arXiv: 1405.7016.

    Article  ADS  Google Scholar 

  16. K. Belczynski, D. E. Holz, T. Bulik, and R. OShaughnessy, Nature 534, 512 (2016), arXiv: 1602.04531.

    Article  ADS  Google Scholar 

  17. B. P. Abbott, et al. (LIGO Scientific and Virgo Collaborations), Astrophys. J. 818, L22 (2016), arXiv: 1602.03846.

    Article  ADS  Google Scholar 

  18. M. C. Miller, Gen. Relativ. Gravit. 48, 95 (2016), arXiv: 1606.06526.

    Article  ADS  Google Scholar 

  19. S. Bird, I. Cholis, J. B. Muñoz, Y. Ali-Haïmoud, M. Kamionkowski, E. D. Kovetz, A. Raccanelli, and A. G. Riess, Phys. Rev. Lett. 116, 201301 (2016), arXiv: 1603.00464.

    Article  ADS  Google Scholar 

  20. S. Clesse, and J. García-Bellido, Phys. Dark Universe 15, 142 (2017), arXiv: 1603.05234.

    Article  ADS  Google Scholar 

  21. M. Sasaki, T. Suyama, T. Tanaka, and S. Yokoyama, Phys. Rev. Lett. 117, 061101 (2016), arXiv: 1603.08338.

    Article  ADS  Google Scholar 

  22. M. Sasaki, T. Suyama, T. Tanaka, and S. Yokoyama, Class. Quantum Grav. 35, 063001 (2018), arXiv: 1801.05235.

    Article  ADS  Google Scholar 

  23. J. García-Bellido, J. F. Nuño Siles, and E. Ruiz Morales, Phys. Dark Universe 31, 100791 (2021), arXiv: 2010.13811.

    Article  Google Scholar 

  24. Y. B. Zel’dovich, and I. D. Novikov, Sov. Astron. 10, 602 (1966).

    ADS  Google Scholar 

  25. S. Hawking, Mon. Not. R. Astron. Soc. 152, 75 (1971).

    Article  ADS  Google Scholar 

  26. B. J. Carr, and S. W. Hawking, Mon. Not. R. Astron. Soc. 168, 399 (1974).

    Article  ADS  Google Scholar 

  27. P. Meszaros, Astron. Astrophys. 37, 225 (1974).

    ADS  Google Scholar 

  28. B. J. Carr, Astrophys. J. 201, 1 (1975).

    Article  ADS  Google Scholar 

  29. T. Bringmann, P. Scott, and Y. Akrami, Phys. Rev. D 85, 125027 (2012), arXiv: 1110.2484.

    Article  ADS  Google Scholar 

  30. A. M. Green, Phys. Rev. D 98, 023529 (2018), arXiv: 1805.05178.

    Article  ADS  Google Scholar 

  31. Y. Akrami, et al. (Planck Collaboration), Astron. Astrophys. 641, A10 (2020), arXiv: 1807.06211.

    Article  Google Scholar 

  32. J. Chluba, A. Kogut, S. P. Patil, M. H. Abitbol, N. Aghanim, Y. Ali-Haimoud, M. A. Amin, J. Aumont, N. Bartolo, K. Basu, E. S. Battistelli, R. Battye, D. Baumann, I. Ben-Dayan, B. Bolliet, J. R. Bond, F. R. Bouchet, C. P. Burgess, C. Burigana, C. T. Byrnes, G. Cabass, D. T. Chuss, S. Clesse, P. S. Cole, L. Dai, P. de Bernardis, J. Delabrouille, V. Desjacques, G. de Zotti, J. A. D. Diacoumis, E. Dimastrogiovanni, E. Di Valentino, J. Dunkley, R. Durrer, C. Dvorkin, J. Ellis, H. K. Eriksen, M. Fasiello, D. Fixsen, F. Finelli, R. Flauger, S. Galli, J. Garcia-Bellido, M. Gervasi, V. Gluscevic, D. Grin, L. Hart, C. Hernandez-Monteagudo, J. C. Hill, D. Jeong, B. R. Johnson, G. Lagache, E. Lee, A. Lewis, M. Liguori, M. Kamionkowski, R. Khatri, K. Kohri, E. Komatsu, K. E. Kunze, A. Mangilli, S. Masi, J. Mather, S. Matarrese, M. A. Miville-Deschenes, T. Montaruli, M. Munchmeyer, S. Mukherjee, T. Nakama, F. Nati, A. Ota, L. A. Page, E. Pajer, V. Poulin, A. Ravenni, C. Reichardt, M. Remazeilles, A. Rotti, J. A. Rubino-Martin, A. Sarkar, S. Sarkar, G. Savini, D. Scott, P. D. Serpico, J. Silk, T. Souradeep, D. N. Spergel, A. A. Starobinsky, R. Subrahmanyan, R. A. Sunyaev, E. Switzer, A. Tartari, H. Tashiro, R. Basu Thakur, T. Trombetti, B. Wallisch, B. D. Wandelt, I. K. Wehus, E. J. Wollack, M. Zaldarriaga, and M. Zannoni, Bull. Am. Astron. Soc. 51, 184 (2019).

    Google Scholar 

  33. D. Jeong, J. Pradler, J. Chluba, and M. Kamionkowski, Phys. Rev. Lett. 113, 061301 (2014).

    Article  ADS  Google Scholar 

  34. T. Nakama, T. Suyama, and J. Yokoyama, Phys. Rev. Lett. 113, 061302 (2014), arXiv: 1403.5407.

    Article  ADS  Google Scholar 

  35. K. Inomata, M. Kawasaki, and Y. Tada, Phys. Rev. D 94, 043527 (2016), arXiv: 1605.04646.

    Article  ADS  Google Scholar 

  36. R. Allahverdi, M. A. Amin, A. Berlin, N. Bernal, C. T. Byrnes, M. S. Delos, A. L. Erickcek, M. Escudero, D. G. Figueroa, K. Freese, T. Harada, D. Hooper, D. I. Kaiser, T. Karwal, K. Kohri, G. Krnjaci, M. Lewicki, K. D. Lozanov, V. Poulin, K. Sinha, T. L. Smith, T. Takahashi, T. Tenkanen, J. Unwin, and S. Watson, Open J. Astrophys. 4, 1 (2021), arXiv: 2006.16182.

    Article  Google Scholar 

  37. A. D. Gow, C. T. Byrnes, P. S. Cole, and S. Young, J. Cosmol. Astropart. Phys. 2021, 2 (2021), arXiv: 2008.03289.

    Article  Google Scholar 

  38. G. Franciolini, and A. Urbano, Phys. Rev. D 106, 123519 (2022), arXiv: 2207.10056.

    Article  ADS  Google Scholar 

  39. G. Franciolini, I. Musco, P. Pani, and A. Urbano, Phys. Rev. D 106, 123526 (2022), arXiv: 2209.05959.

    Article  ADS  Google Scholar 

  40. R. Kimura, T. Suyama, M. Yamaguchi, and Y. Zhang, J. Cosmol. Astropart. Phys. 2021, 31 (2021), arXiv: 2102.05280.

    Article  Google Scholar 

  41. M. Raidal, C. Spethmann, V. Vaskonen, and H. Veermäe, J. Cosmol. Astropart. Phys. 2019, 18 (2019).

    Article  Google Scholar 

  42. V. De Luca, G. Franciolini, P. Pani, and A. Riotto, J. Cosmol. Astropart. Phys. 2020, 52 (2020), arXiv: 2003.02778.

    Article  Google Scholar 

  43. I. Musco, J. C. Miller, and L. Rezzolla, Class. Quantum Grav. 22, 1405 (2005), arXiv: gr-qc/0412063.

    Article  ADS  Google Scholar 

  44. I. Musco, J. C. Miller, and A. G. Polnarev, Class. Quantum Grav. 26, 235001 (2009), arXiv: 0811.1452.

    Article  ADS  Google Scholar 

  45. I. Musco, and J. C. Miller, Class. Quantum Grav. 30, 145009 (2013), arXiv: 1201.2379.

    Article  ADS  Google Scholar 

  46. T. Harada, C. M. Yoo, and K. Kohri, Phys. Rev. D 89, 029903 (2014).

    Article  ADS  Google Scholar 

  47. C. M. Yoo, T. Harada, J. Garriga, and K. Kohri, Prog. Theor. Exp. Phys. 2018, 123E01 (2018), arXiv: 1805.03946.

    Article  Google Scholar 

  48. I. Musco, Phys. Rev. D 100, 123524 (2019), arXiv: 1809.02127.

    Article  ADS  MathSciNet  Google Scholar 

  49. Y. Ali-Haïmoud, and M. Kamionkowski, Phys. Rev. D 95, 043534 (2017), arXiv: 1612.05644.

    Article  ADS  Google Scholar 

  50. V. Poulin, P. D. Serpico, F. Calore, S. Clesse, and K. Kohri, Phys. Rev. D 96, 083524 (2017), arXiv: 1707.04206.

    Article  ADS  Google Scholar 

  51. P. D. Serpico, V. Poulin, D. Inman, and K. Kohri, Phys. Rev. Res. 2, 023204 (2020), arXiv: 2002.10771.

    Article  Google Scholar 

  52. A. M. Green, A. R. Liddle, K. A. Malik, and M. Sasaki, Phys. Rev. D 70, 041502 (2004), arXiv: astro-ph/0403181.

    Article  ADS  Google Scholar 

  53. B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, Rep. Prog. Phys. 84, 116902 (2021), arXiv: 2002.12778.

    Article  ADS  Google Scholar 

  54. M. W. Choptuik, Phys. Rev. Lett. 70, 9 (1993).

    Article  ADS  Google Scholar 

  55. G. Domenech, Universe 7, 398 (2021), arXiv: 2109.01398.

    Article  ADS  Google Scholar 

  56. S. Pi, and M. Sasaki, arXiv: 2112.12680.

  57. Z. Arzoumanian, et al. (NANOGrav Collaboration), Astrophys. J. Lett. 905, L34 (2020), arXiv: 2009.04496.

    Article  ADS  Google Scholar 

  58. V. Vaskonen, and H. Veermäe, Phys. Rev. Lett. 126, 051303 (2021), arXiv: 2009.07832.

    Article  ADS  Google Scholar 

  59. V. De Luca, G. Franciolini, and A. Riotto, Phys. Rev. Lett. 126, 041303 (2021), arXiv: 2009.08268.

    Article  ADS  Google Scholar 

  60. K. Kohri, and T. Terada, Phys. Lett. B 813, 136040 (2021), arXiv: 2009.11853.

    Article  Google Scholar 

  61. Z. Yi, and Z. H. Zhu, J. Cosmol. Astropart. Phys. 2022, 46 (2022).

    Article  Google Scholar 

  62. K. Ando, K. Inomata, and M. Kawasaki, Phys. Rev. D 97, 103528 (2018), arXiv: 1802.06393.

    Article  ADS  Google Scholar 

  63. S. Young, Int. J. Mod. Phys. D 29, 2030002 (2020), arXiv: 1905.01230.

    Article  ADS  Google Scholar 

  64. A. Hall, A. D. Gow, and C. T. Byrnes, Phys. Rev. D 102, 123524 (2020), arXiv: 2008.13704.

    Article  ADS  Google Scholar 

  65. K. W. K. Wong, G. Franciolini, V. De Luca, V. Baibhav, E. Berti, P. Pani, and A. Riotto, Phys. Rev. D 103, 023026 (2021), arXiv: 2011.01865.

    Article  ADS  Google Scholar 

  66. M. Zevin, S. S. Bavera, C. P. L. Berry, V. Kalogera, T. Fragos, P. Marchant, C. L. Rodriguez, F. Antonini, D. E. Holz, and C. Pankow, Astrophys. J. 910, 152 (2021), arXiv: 2011.10057.

    Article  ADS  Google Scholar 

  67. G. Hütsi, M. Raidal, V. Vaskonen, and H. Veermäe, J. Cosmol. Astropart. Phys. 2021, 68 (2021), arXiv: 2012.02786.

    Article  Google Scholar 

  68. K. Kritos, V. De Luca, G. Franciolini, A. Kehagias, and A. Riotto, J. Cosmol. Astropart. Phys. 2021, 39 (2021).

    Article  Google Scholar 

  69. G. Franciolini, V. Baibhav, V. De Luca, K. K. Y. Ng, K. W. Y. Wong, E. Berti, P. Pani, A. Riotto, and S. Vitale, Phys. Rev. D 105, 083526 (2022).

    Article  ADS  Google Scholar 

  70. S. S. Bavera, G. Franciolini, G. Cusin, A. Riotto, M. Zevin, and T. Fragos, Astron. Astrophys. 660, A26 (2022), arXiv: 2109.05836.

    Article  ADS  Google Scholar 

  71. Z. C. Chen, C. Yuan, and Q. G. Huang, Phys. Lett. B 829, 137040 (2022), arXiv: 2108.11740.

    Article  Google Scholar 

  72. H. Y. Chen, D. E. Holz, J. Miller, M. Evans, S. Vitale, and J. Creighton, Class. Quantum Grav. 38, 055010 (2021), arXiv: 1709.08079.

    Article  ADS  Google Scholar 

  73. S. Okano, and T. Suyama, arXiv: 2201.10258.

  74. X. Luo, and D. N. Schramm, Astrophys. J. 408, 33 (1993).

    Article  ADS  Google Scholar 

  75. L. Verde, L. Wang, A. F. Heavens, and M. Kamionkowski, Mon. Not. R. Astron. Soc. 313, 141 (2000), arXiv: astro-ph/9906301.

    Article  ADS  Google Scholar 

  76. L. Verde, R. Jimenez, M. Kamionkowski, and S. Matarrese, Mon. Not. R. Astron. Soc. 325, 412 (2001), arXiv: astro-ph/0011180.

    Article  ADS  Google Scholar 

  77. E. Komatsu, and D. N. Spergel, Phys. Rev. D 63, 063002 (2001), arXiv: astro-ph/0005036.

    Article  ADS  Google Scholar 

  78. N. Bartolo, E. Komatsu, S. Matarrese, and A. Riotto, Phys. Rep. 402, 103 (2004), arXiv: astro-ph/0406398.

    Article  ADS  MathSciNet  Google Scholar 

  79. L. Boubekeur, and D. H. Lyth, Phys. Rev. D 73, 021301 (2006), arXiv: astro-ph/0504046.

    Article  ADS  Google Scholar 

  80. C. T. Byrnes, K. Koyama, M. Sasaki, and D. Wands, J. Cosmol. Astropart. Phys. 2007, 27 (2007), arXiv: 0705.4096.

    Article  Google Scholar 

  81. J. S. Bullock, and J. R. Primack, Phys. Rev. D 55, 7423 (1997), arXiv: astro-ph/9611106.

    Article  ADS  Google Scholar 

  82. P. Ivanov, Phys. Rev. D 57, 7145 (1998), arXiv: astro-ph/9708224.

    Article  ADS  MathSciNet  Google Scholar 

  83. P. P. Avelino, Phys. Rev. D 72, 124004 (2005), arXiv: astro-ph/0510052.

    Article  ADS  Google Scholar 

  84. D. H. Lyth, J. Cosmol. Astropart. Phys. 2012, 22 (2012), arXiv: 1201.4312.

    Article  Google Scholar 

  85. C. T. Byrnes, E. J. Copeland, and A. M. Green, Phys. Rev. D 86, 043512 (2012), arXiv: 1206.4188.

    Article  ADS  Google Scholar 

  86. S. Shandera, A. L. Erickcek, P. Scott, and J. Y. Galarza, Phys. Rev. D 88, 103506 (2013), arXiv: 1211.7361.

    Article  ADS  Google Scholar 

  87. S. Young, and C. T. Byrnes, J. Cosmol. Astropart. Phys. 2013, 052 (2013), arXiv: 1307.4995.

    Article  Google Scholar 

  88. S. Young, and C. T. Byrnes, Phys. Rev. D 91, 083521 (2015), arXiv: 1411.4620.

    Article  ADS  Google Scholar 

  89. S. Young, D. Regan, and C. T. Byrnes, J. Cosmol. Astropart. Phys. 2016, 29 (2016), arXiv: 1512.07224.

    Article  Google Scholar 

  90. G. Franciolini, A. Kehagias, S. Matarrese, and A. Riotto, J. Cosmol. Astropart. Phys. 2018, 16 (2018).

    Article  Google Scholar 

  91. R. G. Cai, S. Pi, and M. Sasaki, Phys. Rev. Lett. 122, 201101 (2019), arXiv: 1810.11000.

    Article  ADS  Google Scholar 

  92. V. D. Luca, G. Franciolini, A. Kehagias, M. Peloso, A. Riotto, and C. Ünal, J. Cosmol. Astropart. Phys. 2019, 48 (2019), arXiv: 1904.00970.

    Article  Google Scholar 

  93. S. Young, I. Musco, and C. T. Byrnes, J. Cosmol. Astropart. Phys. 2019, 12 (2019), arXiv: 1904.00984.

    Article  Google Scholar 

  94. V. Atal, J. Cid, A. Escrivá, and J. Garriga, J. Cosmol. Astropart. Phys. 2020, 22 (2020).

    Article  Google Scholar 

  95. C. M. Yoo, J. O. Gong, and S. Yokoyama, J. Cosmol. Astropart. Phys. 2019, 33 (2019), arXiv: 1906.06790.

    Article  Google Scholar 

  96. J. M. Ezquiaga, J. García-Bellido, and V. Vennin, J. Cosmol. Astropart. Phys. 2020, 29 (2020), arXiv: 1912.05399.

    Article  Google Scholar 

Download references

Author information

Author notes

  1. These authors contributed equally to this work.

Authors and Affiliations

  1. School of Physics Science and Engineering, Tongji University, Shanghai, 200092, China

    Xinpeng Wang & Ying-li Zhang

  2. Institute for Advanced Study of Tongji University, Shanghai, 200092, China

    Ying-li Zhang

  3. Kavli Institute for the Physics and Mathematics of the Universe (WPI), Chiba, 277-8583, Japan

    Ying-li Zhang

  4. Center for Gravitation and Cosmology, Yangzhou University, Yangzhou, 225009, China

    Ying-li Zhang

  5. Waseda Institute for Advanced Study, Waseda University, Tokyo, 169-8050, Japan

    Rampei Kimura

  6. Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan

    Masahide Yamaguchi

Authors
  1. Xinpeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying-li Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rampei Kimura
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Masahide Yamaguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ying-li Zhang.

Additional information

M. Yamaguchi acknowledges the support from JSPS Grant-in-Aid for Scientific Research (Grant Nos. JP18K18764, JP21H01080, and JP21H00069), and the Fundamental Research Funds for the Central Universities. We thank Kazunori Kohri, Shi Pi, Misao Sasaki and Teruaki Suyama for useful discussions.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Zhang, Yl., Kimura, R. et al. Reconstruction of power spectrum of primordial curvature perturbations on small scales from primordial black hole binaries scenario of LIGO/VIRGO detection. Sci. China Phys. Mech. Astron. 66, 260462 (2023). https://doi.org/10.1007/s11433-023-2091-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-023-2091-x

Keywords

Search

Navigation