这是indexloc提供的服务，不要输入任何密码
Skip to main content
Springer Nature Link
Log in

Combining strongly lensed and unlensed fast radio bursts: To be a more precise late-universe probe

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

Abstract

The Macquart relation and time-delay cosmography are now two promising ways to fast radio burst (FRB) cosmology. In this work, we propose a joint method that combines strongly lensed and unlensed FRBs for improving cosmological parameter estimation using simulated FRB data from the future sensitive coherent all-sky monitor survey, which is expected to detect a large number of FRBs including galaxy-galaxy strongly lensed events. We find that using a detectable sample of 100000 localized FRBs including 40 lensed events can simultaneously constrain the Hubble constant and the equation of state of dark energy, with high precision of ε(H0) = 0.4% and ε(w) = 4.5% in the simplest dynamical dark energy model. The joint analysis of unlensed and lensed FRBs significantly improves the constraint on H0, which could be more effective than combining either the unlensed FRBs with future gravitational wave (GW) standard sirens or the lensed FRBs with CMB. Furthermore, combining the full FRB sample with the CMB+BAO+SNe data yields σ(H0) = 0.29 km s−1 Mpc−1, σ(w0) = 0.046, and σ(wa) = 0.15 in the two-parameter dynamical dark energy model, which outperforms the results from the CMB+BAO+SNe+GW data. This reinforces the cosmological implications of a multi-wavelength observational strategy in optical and radio bands. We conclude that the future FRB observations will shed light on the nature of dark energy and also the Hubble tension if enough events with long-duration lensing are incorporated.

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

Access this article

Log in via an institution

Subscribe and save

Springer+
from $39.99 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.

References

  1. D. N. Spergel, L. Verde, H. V. Peiris, E. Komatsu, M. R. Nolta, C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, et al., Astrophys. J. Suppl. 148, 175 (2003), arXiv: astro-ph/0302209.

    Article  ADS  Google Scholar 

  2. C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, L. Page, D. N. Spergel, G. S. Tucker, et al., Astrophys. J. Suppl. 148, 1 (2003), arXiv: astro-ph/0302207.

    Article  ADS  Google Scholar 

  3. N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, et al., Astron. Astrophys. 641, A6 (2020).

    Article  Google Scholar 

  4. S. Weinberg, Rev. Mod. Phys. 61, 1 (1989).

    Article  ADS  Google Scholar 

  5. A. Joyce, B. Jain, J. Khoury, and M. Trodden, Phys. Rep. 568, 1 (2015), arXiv: 1407.0059.

    Article  ADS  MathSciNet  Google Scholar 

  6. A. G. Adame, et al. (DESI Collaboration), arXiv: 2404.03002.

  7. A. G. Riess, W. Yuan, L. M. Macri, D. Scolnic, D. Brout, S. Casertano, D. O. Jones, Y. Murakami, G. S. Anand, L. Breuval, et al., Astrophys. J. Lett. 934, L7 (2022), arXiv: 2112.04510.

    Article  ADS  Google Scholar 

  8. L. Verde, T. Treu, and A. G. Riess, Nat. Astron. 3, 891 (2019), arXiv: 1907.10625.

    Article  ADS  Google Scholar 

  9. J. P. Hu, and F. Y. Wang, Universe 9, 94 (2023), arXiv: 2302.05709.

    Article  ADS  Google Scholar 

  10. B. Follin, and L. Knox, Mon. Not. R. Astron. Soc. 477, 4534 (2018), arXiv: 1707.01175.

    Article  ADS  Google Scholar 

  11. W. Yang, S. Pan, E. D. Valentino, R. C. Nunes, S. Vagnozzi, and D. F. Mota, J. Cosmol. Astropart. Phys. 9, 019 (2018), arXiv: 1805.08252.

    Article  ADS  Google Scholar 

  12. R.-Y. Guo, J.-F. Zhang, and X. Zhang, arXiv: 1809.02340.

  13. X. Zhang, and Q. G. Huang, Sci. China-Phys. Mech. Astron. 63, 290402 (2020), arXiv: 1911.09439.

    Article  ADS  Google Scholar 

  14. L. Feng, D. Z. He, H. L. Li, J. F. Zhang, and X. Zhang, Sci. China-Phys. Mech. Astron. 63, 290404 (2020), arXiv: 1910.03872.

    Article  ADS  Google Scholar 

  15. M. X. Liu, Z. Q. Huang, X. L. Luo, H. T. Miao, N. K. Singh, and L. Huang, Sci. China-Phys. Mech. Astron. 63, 290405 (2020), arXiv: 1912.00190.

    Article  ADS  Google Scholar 

  16. S. Vagnozzi, Phys. Rev. D 102, 023518 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  17. L.-Y. Gao, Z.-W. Zhao, S.-S. Xue, and X. Zhang, arXiv: 2101.10714.

  18. R.-G. Cai, Z.-K. Guo, L. Li, S.-J. Wang, and W.-W. Yu, Phys. Rev. D 103, 121302 (2021), arXiv: 2102.02020.

    Article  ADS  Google Scholar 

  19. S. Vagnozzi, Universe 9, 393 (2023), arXiv: 2308.16628.

    Article  ADS  Google Scholar 

  20. M. Moresco, L. Amati, L. Amendola, S. Birrer, J. P. Blakeslee, M. Cantiello, A. Cimatti, J. Darling, M. Della Valle, M. Fishbach, et al., Living Rev Relativ 25, 6 (2022), arXiv: 2201.07241.

    Article  ADS  Google Scholar 

  21. P.-J. Wu, Y. Shao, S.-J. Jin, and X. Zhang, J. Cosmol. Astropart. Phys. 6, 052 (2023), arXiv: 2202.09726.

    Article  ADS  Google Scholar 

  22. X. Zhang, Sci. China-Phys. Mech. Astron. 62, 110431 (2019), arXiv: 1905.11122.

    Article  ADS  Google Scholar 

  23. Y. D. Xu, and X. Zhang, Sci. China-Phys. Mech. Astron. 63, 270431 (2020), arXiv: 2002.00572.

    Article  ADS  Google Scholar 

  24. P. J. Wu, Y. Li, J. F. Zhang, and X. Zhang, Sci. China-Phys. Mech. Astron. 66, 270413 (2023), arXiv: 2212.07681.

    Article  ADS  Google Scholar 

  25. D. R. Lorimer, M. Bailes, M. A. McLaughlin, D. J. Narkevic, and F. Crawford, Science 318, 777 (2007).

    Article  ADS  Google Scholar 

  26. M. Bailes, Science 378, abj3043 (2022), arXiv: 2211.06048.

    Article  ADS  Google Scholar 

  27. B. Zhang, Rev. Mod. Phys. 95, 035005 (2023), arXiv: 2212.03972.

    Article  ADS  Google Scholar 

  28. K. Bandura, G. E. Addison, M. Amiri, J. R. Bond, D. CampbellWilson, L. Connor, J.-F. Cliche, G. Davis, M. Deng, N. Denman, et al., arXiv: 1406.2288.

  29. M. Amiri, B. C. Andersen, K. Bandura, S. Berger, M. Bhardwaj, M. M. Boyce, P. J. Boyle, C. Brar, D. Breitman, T. Cassanelli, et al., Astrophys. J. Suppl. Ser. 257, 59 (2021), arXiv: 2106.04352.

    Article  ADS  Google Scholar 

  30. D. Li, P. Wang, W. W. Zhu, B. Zhang, X. X. Zhang, R. Duan, Y. K. Zhang, Y. Feng, N. Y. Tang, S. Chatterjee, et al., Nature 598, 267 (2021), arXiv: 2107.08205.

    Article  ADS  Google Scholar 

  31. H. Xu, J. R. Niu, P. Chen, K. J. Lee, W. W. Zhu, S. Dong, B. Zhang, J. C. Jiang, B. J. Wang, J. W. Xu, et al., Nature 609, 685 (2022), arXiv: 2111.11764.

    Article  ADS  Google Scholar 

  32. Z. W. Wu, R. A. Main, W. W. Zhu, B. Zhang, P. Jiang, J. R. Niu, J. L. Han, D. Li, K. J. Lee, D. Z. Li, et al., Sci. China-Phys. Mech. Astron. 67, 219512 (2024).

    Article  ADS  Google Scholar 

  33. Z.-G. Dai, Sci. China-Phys. Mech. Astron. 66, 120431 (2023).

    Article  ADS  Google Scholar 

  34. S. Bhandari, and C. Flynn, Universe 7, 85 (2021).

    Article  ADS  Google Scholar 

  35. D. Xiao, F. Y. Wang, and Z. G. Dai, Sci. China-Phys. Mech. Astron. 64, 249501 (2021), arXiv: 2101.04907.

    Article  ADS  Google Scholar 

  36. Q. Wu, and F.-Y. Wang, Chin. Phys. Lett. 41, 119801 (2024), arXiv: 2409.13247.

    Article  ADS  Google Scholar 

  37. J. P. Macquart, J. X. Prochaska, M. McQuinn, K. W. Bannister, S. Bhandari, C. K. Day, A. T. Deller, R. D. Ekers, C. W. James, L. Marnoch, et al., Nature 581, 391 (2020), arXiv: 2005.13161.

    Article  ADS  Google Scholar 

  38. B. Zhou, X. Li, T. Wang, Y. Z. Fan, and D. M. Wei, Phys. Rev. D 89, 107303 (2014), arXiv: 1401.2927.

    Article  ADS  Google Scholar 

  39. H. Gao, Z. Li, and B. Zhang, Astrophys. J. 788, 189 (2014), arXiv: 1402.2498.

    Article  ADS  Google Scholar 

  40. C. W. James, J. X. Prochaska, J. P. Macquart, F. O. North-Hickey, K. W. Bannister, and A. Dunning, Mon. Not. R. Astron. Soc. 509, 4775 (2021), arXiv: 2101.08005.

    Article  ADS  Google Scholar 

  41. K. W. Masui, and K. Sigurdson, Phys. Rev. Lett. 115,121301 (2015), arXiv: 1506.01704.

  42. P. Kumar, and E. V. Linder, Phys. Rev. D 100, 083533 (2019), arXiv: 1903.08175.

    Article  ADS  Google Scholar 

  43. J. G. Zhang, Z. W. Zhao, Y. Li, J. F. Zhang, D. Li, and X. Zhang, Sci. China-Phys. Mech. Astron. 66, 120412 (2023), arXiv: 2307.01605.

    Article  ADS  Google Scholar 

  44. T. Hashimoto, T. Goto, T. Y. Lu, A. Y. L. On, D. J. D. Santos, S. J. Kim, E. K. Eser, S. C. C. Ho, T. Y. Y. Hsiao, and L. Y. W. Lin, Mon. Not. R. Astron. Soc. 502, 2346 (2021), arXiv: 2101.08798.

    Article  ADS  Google Scholar 

  45. J.-J. Wei, and C.-Y. Gao, arXiv: 2409.01543.

  46. Z. W. Zhao, Z. X. Li, J. Z. Qi, H. Gao, J. F. Zhang, and X. Zhang, Astrophys. J. 903, 83 (2020), arXiv: 2006.01450.

    Article  ADS  Google Scholar 

  47. X.-W. Qiu, Z.-W. Zhao, L.-F. Wang, J.-F. Zhang, and X. Zhang, arXiv: 2108.04127.

  48. Z.-W. Zhao, L.-F. Wang, J.-G. Zhang, J.-F. Zhang, and X. Zhang, arXiv: 2210.07162.

  49. M. Jaroszynski, Mon. Not. R. Astron. Soc. 484, 1637 (2019), arXiv: 1812.11936.

    Article  ADS  Google Scholar 

  50. J. J. Wei, X. F. Wu, and H. Gao, Astrophys. J. Lett. 860, L7 (2018), arXiv: 1805.12265.

    Article  ADS  Google Scholar 

  51. A. Walters, A. Weltman, B. M. Gaensler, Y. Z. Ma, and A. Witzemann, Astrophys. J. 856, 65 (2018), arXiv: 1711.11277.

    Article  ADS  Google Scholar 

  52. C. Zhu, and J. Zhang, Phys. Rev. D 106, 023513 (2022), arXiv: 2205.03867.

    Article  ADS  Google Scholar 

  53. S. Hagstotz, R. Reischke, and R. Lilow, Mon. Not. R. Astron. Soc. 511, 662 (2022), arXiv: 2104.04538.

    Article  ADS  Google Scholar 

  54. Q. Wu, G. Q. Zhang, and F. Y. Wang, Mon. Not. R. Astron. Soc.-Lett. 515, L1 (2022), arXiv: 2108.00581.

    Article  ADS  Google Scholar 

  55. C. W. James, E. M. Ghosh, J. X. Prochaska, K. W. Bannister, S. Bhandari, C. K. Day, A. T. Deller, M. Glowacki, A. C. Gordon, K. E. Heintz, et al., Mon. Not. R. Astron. Soc. 516, 4862 (2022), arXiv: 2208.00819.

    Article  ADS  Google Scholar 

  56. J. J. Wei, and F. Melia, Astrophys. J. 955, 101 (2023), arXiv: 2308.05918.

    Article  ADS  Google Scholar 

  57. J. A. S. Fortunata, D. J. Bacon, W. S. Hipolito-Ricaldi, and D. Wands, arXiv: 2407.03532.

  58. S. Kalita, S. Bhatporia, and A. Weltman, arXiv: 2410.01974.

  59. Z.-W. Zhao, J.-G. Zhang, Y. Li, J.-M. Zou, J.-F. Zhang, and X. Zhang, arXiv: 2212.13433.

  60. Y. Liu, H. Yu, and P. Wu, Astrophys. J. Lett. 946, L49 (2023), arXiv: 2210.05202.

    Article  ADS  Google Scholar 

  61. J. Gao, Z. Zhou, M. Du, R. Zou, J. Hu, and L. Xu, Mon. Not. R. Astron. Soc. 527, 7861 (2024), arXiv: 2307.08285.

    Article  ADS  Google Scholar 

  62. Z. X. Li, H. Gao, X. H. Ding, G. J. Wang, and B. Zhang, Nat. Commun. 9, 3833 (2018), arXiv: 1708.06357.

    Article  ADS  Google Scholar 

  63. L. Dai, and W. Lu, Astrophys. J. 847, 19 (2017), arXiv: 1706.06103.

    Article  ADS  Google Scholar 

  64. A. Zitrin, and D. Eichler, Astrophys. J. 866, 101 (2018), arXiv: 1807.03287.

    Article  ADS  Google Scholar 

  65. B. Liu, Z. Li, H. Gao, and Z. H. Zhu, Phys. Rev. D 99, 123517 (2019), arXiv: 1907.10488.

    Article  ADS  Google Scholar 

  66. O. Wucknitz, L. G. Spitler, and U. L. Pen, Astron. Astrophys. 645, A44 (2021), arXiv: 2004.11643.

    Article  ADS  Google Scholar 

  67. T. Adi, and E. D. Kovetz, Phys. Rev. D 104, 103515 (2021), arXiv: 2109.00403.

    Article  ADS  Google Scholar 

  68. S. Zhao, B. Liu, Z. Li, and H. Gao, Astrophys. J. 916, 70 (2021).

    Article  ADS  Google Scholar 

  69. X. Er, and S. Mao, Mon. Not. R. Astron. Soc. 516, 2218 (2022), arXiv: 2208.08208.

    Article  ADS  Google Scholar 

  70. R. Gao, Z. Li, and H. Gao, Mon. Not. R. Astron. Soc. 516, 1977 (2022), arXiv: 2208.10175.

    Article  ADS  Google Scholar 

  71. H. Xiao, L. Dai, and M. McQuinn, Phys. Rev. D 106, 103033 (2022), arXiv: 2206.13534.

    Article  ADS  Google Scholar 

  72. X. Jiang, X. Ren, Z. Li, Y. F. Cai, and X. Er, Mon. Not. R. Astron. Soc. 528, 1965 (2024), arXiv: 2401.05464.

    Article  ADS  Google Scholar 

  73. S. Refsdal, Mon. Not. R. Astron. Soc. 128, 307 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  74. S. Birrer, M. Millon, D. Sluse, A. J. Shajib, F. Courbin, S. Erickson, L. V. E. Koopmans, S. H. Suyu, and T. Treu, Space Sci Rev 220, 48 (2024), arXiv: 2210.10833.

    Article  ADS  Google Scholar 

  75. L. Connor, and V. Ravi, Mon. Not. R. Astron. Soc. 521, 4024 (2023), arXiv: 2206.14310.

    Article  ADS  Google Scholar 

  76. T. Treu, and A. J. Shajib, arXiv: 2307.05714.

  77. B. Wang, J. Z. Qi, J. F. Zhang, and X. Zhang, Astrophys. J. 898, 100 (2020), arXiv: 1910.12173.

    Article  ADS  Google Scholar 

  78. L. F. Wang, J. H. Zhang, D. Z. He, J. F. Zhang, and X. Zhang, Mon. Not. R. Astron. Soc. 514, 1433 (2022), arXiv: 2102.09331.

    Article  ADS  Google Scholar 

  79. J.-Z. Qi, Y. Cui, W.-H. Hu, J.-F. Zhang, J.-L. Cui, and X. Zhang, arXiv: 2202.01396.

  80. J. Z. Qi, W. H. Hu, Y. Cui, J. F. Zhang, and X. Zhang, Universe 8, 254 (2022), arXiv: 2203.10862.

    Article  ADS  Google Scholar 

  81. X. Li, R. E. Keeley, A. Shafieloo, and K. Liao, Astrophys. J. 960, 103 (2024), arXiv: 2308.06951.

    Article  ADS  Google Scholar 

  82. T. Li, T. E. Collett, C. M. Krawczyk, and W. Enzi, Mon. Not. R. Astron. Soc. 527, 5311 (2023), arXiv: 2307.09271.

    Article  ADS  Google Scholar 

  83. S. Cao, J. Qi, M. Biesiada, X. Zheng, T. Xu, and Z. H. Zhu, Astrophys. J. 867, 50 (2018), arXiv: 1810.01287.

    Article  ADS  Google Scholar 

  84. J. Z. Qi, S. Cao, S. Zhang, M. Biesiada, Y. Wu, and Z. H. Zhu, Mon. Not. R. Astron. Soc. 483, 1104 (2019), arXiv: 1803.01990.

    Article  ADS  Google Scholar 

  85. X. H. Liu, Z. H. Li, J. Z. Qi, and X. Zhang, Astrophys. J. 927, 28 (2022), arXiv: 2109.02291.

    Article  ADS  Google Scholar 

  86. J. Z. Qi, Y. F. Jiang, W. T. Hou, and X. Zhang, Astrophys. J. 979, 2 (2025), arXiv: 2407.07336.

    Article  ADS  Google Scholar 

  87. J. B. Mufioz, E. D. Kovetz, L. Dai, and M. Kamionkowski, arXiv: 1605.00008.

  88. R. Laha, Phys. Rev. D 102, 023016 (2020), arXiv: 1812.11810.

    Article  ADS  Google Scholar 

  89. K. Liao, S. B. Zhang, Z. Li, and H. Gao, Astrophys. J. Lett. 896, L11 (2020), arXiv: 2003.13349.

    Article  ADS  Google Scholar 

  90. H. Zhou, Z. Li, Z. Huang, H. Gao, and L. Huang, Mon. Not. R. Astron. Soc. 511, 1141 (2022), arXiv: 2103.08510.

    Article  ADS  Google Scholar 

  91. H. Zhou, Z. Li, K. Liao, C. Niu, H. Gao, Z. Huang, L. Huang, and B. Zhang, Astrophys. J. 928, 124 (2022), arXiv: 2109.09251.

    Article  ADS  Google Scholar 

  92. A. Tsai, D. L. Jow, D. Baker, and U. L. Pen, Phys. Rev. D 110, 043503 (2024), arXiv: 2308.10830.

    Article  ADS  Google Scholar 

  93. H. Xiao, L. Dai, and M. McQuinn, Phys. Rev. D 110, 023516 (2024), arXiv: 2401.08862.

    Article  ADS  Google Scholar 

  94. X. Ding, K. Liao, S. Birrer, A. J. Shajib, T. Treu, and L. Yang, Mon. Not. R. Astron. Soc. 504, 5621 (2021), arXiv: 2103.08609.

    Article  ADS  Google Scholar 

  95. P. Schneider, and D. Sluse, Astron. Astrophys. 564, A103 (2014).

    Article  ADS  Google Scholar 

  96. J. Wagner, Astron. Astrophys. 620, A86 (2018), arXiv: 1809.03505.

    Article  ADS  Google Scholar 

  97. J. Wagner, J. Liesenborgs, and D. Eichler, Astron. Astrophys. 621, A91 (2019), arXiv: 1811.10618.

    Article  ADS  Google Scholar 

  98. L. Wisotzki, P. L. Schechter, H. V. Bradt, J. Heinmüller, and D. Reimers, Astron. Astrophys. 395, 17 (2002), arXiv: astroph/0207062.

    Article  ADS  Google Scholar 

  99. O. Tihhonova, F. Courbin, D. Harvey, S. Hilbert, C. E. Rusu, C. D. Fassnacht, V. Bonvin, P. J. Marshall, G. Meylan, D. Sluse, et al., Mon. Not. R. Astron. Soc. 477, 5657 (2018), arXiv: 1711.08804.

    Article  ADS  Google Scholar 

  100. G. C. F. Chen, C. D. Fassnacht, S. H. Suyu, C. E. Rusu, J. H. H. Chan, K. C. Wong, M. W. Auger, S. Hilbert, V. Bonvin, S. Birrer, et al., Mon. Not. R. Astron. Soc. 490, 1743 (2019), arXiv: 1907.02533.

    Article  ADS  Google Scholar 

  101. S. H. Suyu, S. Huber, R. Canameras, M. Kromer, S. Schuldt, S. Taubenberger, A. Yildirim, V. Bonvin, J. H. H. Chan, F. Courbin, et al., Astron. Astrophys. 644, A162 (2020), arXiv: 2002.08378.

    Article  ADS  Google Scholar 

  102. M. Oguri, Rep. Prog. Phys. 82, 126901 (2019), arXiv: 1907.06830.

    Article  ADS  MathSciNet  Google Scholar 

  103. K. Liao, M. Biesiada, and Z. H. Zhu, Chin. Phys. Lett. 39, 119801 (2022), arXiv: 2207.13489.

    Article  ADS  Google Scholar 

  104. J. M. Cordes, and T. J. W. Lazio, arXiv: astro-ph/0207156.

  105. J. M. Yao, R. N. Manchester, and N. Wang, Astrophys. J. 835, 29 (2017).

    Article  ADS  Google Scholar 

  106. K. Dolag, B. M. Gaensler, A. M. Beck, and M. C. Beck, Mon. Not. R. Astron. Soc. 451, 4277 (2015), arXiv: 1412.4829.

    Article  ADS  Google Scholar 

  107. J. X. Prochaska, and Y. Zheng, Mon. Not. R. Astron. Soc. 485, (2019).

  108. A. A. Meiksin, Rev. Mod. Phys. 81, 1405 (2009), arXiv: 0711.3358.

    Article  ADS  Google Scholar 

  109. J. M. Shull, B. D. Smith, and C. W. Danforth, Astrophys. J. 759, 23 (2012), arXiv: 1112.2706.

    Article  ADS  Google Scholar 

  110. T. Lemos, R. Goncalves, J. Carvalho, and J. Alcaniz, Eur. Phys. J. C 83, 1128 (2023), arXiv: 2307.06911.

    Article  ADS  Google Scholar 

  111. J.-J. Wei, Z. Li, H. Gao, and X.-F. Wu, arXiv: 1907.09772.

  112. Z. Li, H. Gao, J. J. Wei, Y. P. Yang, B. Zhang, and Z. H. Zhu, Astrophys. J. 876, 146 (2019), arXiv: 1904.08927.

    Article  ADS  Google Scholar 

  113. Z. Li, H. Gao, J. J. Wei, Y. P. Yang, B. Zhang, and Z. H. Zhu, Mon. Not. R. Astron. Soc.-Lett. 496, L28 (2020), arXiv: 2004.08393.

    Article  ADS  Google Scholar 

  114. J. P. Dai, and J. Q. Xia, Mon. Not. R. Astron. Soc. 503, 4576 (2021), arXiv: 2103.08479.

    Article  ADS  Google Scholar 

  115. B. Wang, and J. J. Wei, Astrophys. J. 944, 50 (2023), arXiv: 2211.02209.

    Article  ADS  Google Scholar 

  116. H. N. Lin, and R. Zou, Mon. Not. R. Astron. Soc. 520, 6237 (2023), arXiv: 2302.10585.

    Article  ADS  Google Scholar 

  117. M. McQuinn, Astrophys. J. Lett. 780, L33 (2013).

    Article  ADS  Google Scholar 

  118. D. C. Qiang, and H. Wei, Phys. Rev. D 103, 083536 (2021), arXiv: 2102.00579.

    Article  ADS  Google Scholar 

  119. C. H. Niu, K. Aggarwal, D. Li, X. Zhang, S. Chatterjee, C. W. Tsai, W. Yu, C. J. Law, S. Burke-Spolaor, J. M. Cordes, et al., Nature 606, 873 (2022), arXiv: 2110.07418.

    Article  ADS  Google Scholar 

  120. G. Q. Zhang, H. Yu, J. H. He, and F. Y. Wang, Astrophys. J. 900, 170 (2020), arXiv: 2007.13935.

    Article  ADS  Google Scholar 

  121. P. Beniamini, P. Kumar, X. Ma, and E. Quataert, Mon. Not. R. Astron. Soc. 502, 5134 (2021), arXiv: 2011.11643.

    Article  ADS  Google Scholar 

  122. M. E. Orr, B. Burkhart, W. Lu, S. B. Ponnada, and C. B. Hummels, Astrophys. J. Lett. 972, L26 (2024), arXiv: 2406.03523.

    Article  ADS  Google Scholar 

  123. C. Chang, S. Zhang, D. Xiao, Z. Tang, Y. Li, J. Wei, and X. Wu, arXiv: 2406.19654.

  124. R. Luo, R. D. Ekers, G. Hobbs, A. Dunning, C. W. James, M. E. Lower, V. Gupta, A. Zic, M. Sokolowski, C. Phillips, et al, arXiv: 2405.07439.

  125. H. H. Lin, K. Lin, C. T. Li, Y. H. Tseng, H. Jiang, J. H. Wang, J. C. Cheng, U. L. Pen, M. T. Chen, P. Chen, et al., Publ. Astron. Soc. Pac. 134, 094106 (2022), arXiv: 2206.08983.

    Article  ADS  Google Scholar 

  126. J. W. Luo, J. M. Zhu-Ge, and B. Zhang, Mon. Not. R. Astron. Soc. 518, 1629 (2022), arXiv: 2210.02463.

    Article  ADS  Google Scholar 

  127. J. M. Zhu-Ge, J. W. Luo, and B. Zhang, Mon. Not. R. Astron. Soc. 519, 1823 (2022), arXiv: 2210.02471.

    Article  ADS  Google Scholar 

  128. F. Kirsten, O. S. Ould-Boukattine, W. Herrmann, M. P. Gawrofiski, J. W. T. Hessels, W. Lu, M. P. Snelders, P. Chawla, J. Yang, R. Blaauw, et al., Nat. Astron. 8, 337 (2024), arXiv: 2306.15505.

    Article  ADS  Google Scholar 

  129. W. P. Sun, J. G. Zhang, Y. Li, W. T. Hou, F. W. Zhang, J. F. Zhang, and X. Zhang, Astrophys. J. 980, 185 (2025), arXiv: 2409.11173.

    Article  ADS  Google Scholar 

  130. B. H. Chen, T. Hashimoto, T. Goto, S. J. Kim, D. J. D. Santos, A. Y. L. On, T. Y. Lu, and T. Y. Y. Hsiao, Mon. Not. R. Astron. Soc. 509, 1227 (2021), arXiv: 2110.09440.

    Article  ADS  Google Scholar 

  131. C. D. Bochenek, V. Ravi, K. V. Belov, G. Hallinan, J. Kocz, S. R. Kulkarni, and D. L. McKenna, arXiv: 2005.10828.

  132. L. Lin, C. F. Zhang, P. Wang, H. Gao, X. Guan, J. L. Han, J. C. Jiang, P. Jiang, K. J. Lee, D. Li, et al., Nature 587, 63 (2020), arXiv: 2005.11479.

    Article  ADS  Google Scholar 

  133. C. K. Li, L. Lin, S. L. Xiong, M. Y. Ge, X. B. Li, T. P. Li, F. J. Lu, S. N. Zhang, Y. L. Tuo, Y. Nang, et al., Nat. Astron. 5, 378 (2021), arXiv: 2005.11071.

    Article  ADS  Google Scholar 

  134. R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, N. Adhikari, R. X. Adhikari, V. B. Adya, C. Affeldt, D. Agarwal, et al., Astrophys. J. 955, 155 (2023), arXiv: 2203.12038.

    Article  ADS  Google Scholar 

  135. A. Moroianu, L. Wen, C. W. James, S. Ai, M. Kovalam, F. H. Panther, and B. Zhang, Nat. Astron. 7, 579 (2023), arXiv: 2212.00201.

    Article  ADS  Google Scholar 

  136. Q.-L. Zhou, Y. Li, J.-J. Geng, Y.-P. Yang, M.-K. Hu, L. Hu, X.-F. Wu, and S. Zheng, Chin. Astron. Astrophys. 48, 100 (2024).

    Article  ADS  Google Scholar 

  137. B. C. Andersen, K. M. Bandura, M. Bhardwaj, A. Bij, M. M. Boyce, P. J. Boyle, C. Brar, T. Cassanelli, P. Chawla, T. Chen, et al., Nature 587, 54 (2020), arXiv: 2005.10324.

    Article  ADS  Google Scholar 

  138. S. C. C. Ho, T. Hashimoto, T. Goto, Y. W. Lin, S. J. Kim, Y. Uno, and T. Y. Y. Hsiao, Astrophys. J. 950, 53 (2023), arXiv: 2304.04990.

    Article  ADS  Google Scholar 

  139. T. E. Collett, Astrophys. J. 811, 20 (2015), arXiv: 1507.02657.

    Article  ADS  Google Scholar 

  140. L. Chen, Q. G. Huang, and K. Wang, J. Cosmol. Astropart. Phys. 2019(2), 028 (2019).

    Article  Google Scholar 

  141. P. Denzel, J. P. Coles, P. Saha, and L. L. R. Williams, Mon. Not. R. Astron. Soc. 501, 784 (2021), arXiv: 2007.14398.

    Article  ADS  Google Scholar 

  142. M. Punturo, M. Abernathy, F. Acernese, B. Allen, N. Andersson, K. Arun, F. Barone, B. Barr, M. Barsuglia, M. Beker, et al., Class. Quantum Grav. 27, 194002 (2010).

    Article  ADS  Google Scholar 

  143. B. F. Schutz, Nature 323, 310 (1986).

    Article  ADS  Google Scholar 

  144. D. E. Holz, and S. A. Hughes, Astrophys. J. 629, 15 (2005), arXiv: astro-ph/0504616.

    Article  ADS  Google Scholar 

  145. B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, V. B. Adya, et al., Nature 551, 85 (2017), arXiv: 1710.05835.

    Article  ADS  Google Scholar 

  146. W. Zhao, C. Van Den Broeck, D. Baskaran, and T. G. F. Li, Phys. Rev. D 83, 023005 (2011), arXiv: 1009.0206.

    Article  ADS  Google Scholar 

  147. H. Y. Chen, M. Fishbach, and D. E. Holz, Nature 562, 545 (2018), arXiv: 1712.06531.

    Article  ADS  Google Scholar 

  148. L. F. Wang, X. N. Zhang, J. F. Zhang, and X. Zhang, Phys. Lett. B 782, 87 (2018), arXiv: 1802.04720.

    Article  ADS  Google Scholar 

  149. X. N. Zhang, L. F. Wang, J. F. Zhang, and X. Zhang, Phys. Rev. D 99, 063510 (2019), arXiv: 1804.08379.

    Article  ADS  Google Scholar 

  150. M. Du, W. Yang, L. Xu, S. Pan, and D. F. Mota, Phys. Rev. D 100, 043535 (2019), arXiv: 1812.01440.

    Article  ADS  Google Scholar 

  151. Z. Chang, Q. G. Huang, S. Wang, and Z. C. Zhao, Eur. Phys. J. C 79, 177 (2019).

    Article  ADS  Google Scholar 

  152. J. F. Zhang, H. Y. Dong, J. Z. Qi, and X. Zhang, Eur. Phys. J. C 80, 217 (2020), arXiv: 1906.07504.

    Article  ADS  Google Scholar 

  153. S.-J. Jin, D.-Z. He, Y. Xu, J.-F. Zhang, and X. Zhang, arXiv: 2001.05393.

  154. S. J. Jin, L. F. Wang, P. J. Wu, J. F. Zhang, and X. Zhang, Phys. Rev. D 104, 103507 (2021), arXiv: 2106.01859.

    Article  ADS  Google Scholar 

  155. M. D. Cao, J. Zheng, J. Z. Qi, X. Zhang, and Z. H. Zhu, Astrophys. J. 934, 108 (2022), arXiv: 2112.14564.

    Article  ADS  Google Scholar 

  156. Y. J. Wang, J. Z. Qi, B. Wang, J. F. Zhang, J. L. Cui, and X. Zhang, Mon. Not. R. Astron. Soc. 516, 5187 (2022), arXiv: 2201.12553.

    Article  ADS  Google Scholar 

  157. S. J. Jin, R. Q. Zhu, L. F. Wang, H. L. Li, J. F. Zhang, and X. Zhang, Commun. Theor. Phys. 74, 105404 (2022), arXiv: 2204.04689.

    Article  ADS  Google Scholar 

  158. S.-J. Jin, T.-N. Li, J.-F. Zhang, and X. Zhang, arXiv: 2202.11882.

  159. T. N. Li, S. J. Jin, H. L. Li, J. F. Zhang, and X. Zhang, Astrophys. J. 963, 52 (2024), arXiv: 2310.15879.

    Article  ADS  Google Scholar 

  160. T. Han, S. J. Jin, J. F. Zhang, and X. Zhang, Eur. Phys. J. C 84, 663 (2024), arXiv: 2309.14965.

    Article  ADS  Google Scholar 

  161. S.-J. Jin, R.-Q. Zhu, J.-Y. Song, T. Han, J.-F. Zhang, and X. Zhang, arXiv: 2309.11900.

  162. L. Feng, T. Han, J. F. Zhang, and X. Zhang, Chin. Phys. C 48, 095104 (2024), arXiv: 2404.19530.

    Article  ADS  Google Scholar 

  163. Y.-Y. Dong, J.-Y. Song, S.-J. Jin, J.-F. Zhang, and X. Zhang, arXiv: 2404.18188.

  164. J. Zheng, X. H. Liu, and J. Z. Qi, Astrophys. J. 975, 215 (2024), arXiv: 2407.05686.

    Article  ADS  Google Scholar 

  165. Q. M. Fu, and X. Zhang, Chin. Phys. C 49, 045101 (2025), arXiv: 2408.01665.

    Article  ADS  Google Scholar 

  166. L. Feng, T. Han, J. F. Zhang, and X. Zhang, Commun. Theor. Phys. 77, 065403 (2025), arXiv: 2409.04453.

    Article  ADS  Google Scholar 

  167. C. Cutler, and D. E. Holz, Phys. Rev. D 80, 104009 (2009), arXiv: 0906.3752.

    Article  ADS  Google Scholar 

  168. R. G. Cai, T. B. Liu, X. W. Liu, S. J. Wang, and T. Yang, Phys. Rev. D 97, 103005 (2018), arXiv: 1712.00952.

    Article  ADS  Google Scholar 

  169. L.-F. Wang, Z.-W. Zhao, J.-F. Zhang, and X. Zhang, arXiv: 1907.01838.

  170. Z. W. Zhao, L. F. Wang, J. F. Zhang, and X. Zhang, Sci. Bull. 65, 1340 (2020), arXiv: 1912.11629.

    Article  Google Scholar 

  171. L. F. Wang, S. J. Jin, J. F. Zhang, and X. Zhang, Sci. China-Phys. Mech. Astron. 65, 210411 (2022), arXiv: 2101.11882.

    Article  ADS  Google Scholar 

  172. Z. K. Guo, Sci. China-Phys. Mech. Astron. 65, 210431 (2022).

    Article  ADS  Google Scholar 

  173. J. Y. Song, L. F. Wang, Y. Li, Z. W. Zhao, J. F. Zhang, W. Zhao, and X. Zhang, Sci. China-Phys. Mech. Astron. 67, 230411 (2024), arXiv: 2212.00531.

    Article  ADS  Google Scholar 

  174. S. J. Jin, Y. Z. Zhang, J. Y. Song, J. F. Zhang, and X. Zhang, Sci. China-Phys. Mech. Astron. 67, 220412 (2024), arXiv: 2305.19714.

    Article  ADS  Google Scholar 

  175. W. Zhao, Sci. China-Phys. Mech. Astron. 67, 220431 (2024).

    Article  ADS  Google Scholar 

  176. Z. H. Zhu, Sci. China-Phys. Mech. Astron. 67, 230431 (2024).

    Article  ADS  Google Scholar 

  177. C. Yan, W. Zhao, and Y. Lu, arXiv: 1912.04103.

  178. L.-F. Wang, Y. Shao, J.-F. Zhang, and X. Zhang, arXiv: 2201.00607.

  179. S.-R. Xiao, Y. Shao, L.-F. Wang, J.-Y. Song, L. Feng, J.-F. Zhang, and X. Zhang, arXiv: 2408.00609.

  180. R. G. Cai, Z. Cao, Z. K. Guo, S. J. Wang, and T. Yang, Natl. Sci. Rev. 4, 687 (2017), arXiv: 1703.00187.

    Article  Google Scholar 

  181. L. Bian, R. G. Cai, S. Cao, Z. Cao, H. Gao, Z. K. Guo, K. Lee, D. Li, J. Liu, Y. Lu, et al., Sci. China-Phys. Mech. Astron. 64, 120401 (2021), arXiv: 2106.10235.

    Article  ADS  Google Scholar 

  182. A. Nishizawa, A. Taruya, and S. Saito, Phys. Rev. D 83, 084045 (2011).

    Article  ADS  Google Scholar 

  183. C. M. Hirata, D. E. Holz, and C. Cutler, Phys. Rev. D 81, 124046 (2010).

    Article  ADS  Google Scholar 

  184. C. Gordon, K. Land, and A. Slosar, Phys. Rev. Lett. 99, 081301 (2007).

    Article  ADS  Google Scholar 

  185. J.-F. Zhang, M. Zhang, S.-J. Jin, J.-Z. Qi, and X. Zhang, arXiv: 1907.03238.

  186. F. Beutler, C. Blake, M. Colless, D. H. Jones, L. Staveley-Smith, L. Campbell, Q. Parker, W. Saunders, and F. Watson, Mon. Not. R. Astron. Soc. 416, 3017 (2011).

    Article  ADS  Google Scholar 

  187. A. J. Ross, L. Samushia, C. Howlett, W. J. Percival, A. Burden, and M. Manera, Mon. Not. R. Astron. Soc. 449, 835 (2015).

    Article  ADS  Google Scholar 

  188. S. Alam, M. Ata, S. Bailey, F. Beutler, D. Bizyaev, J. A. Blazek, A. S. Bolton, J. R. Brownstein, A. Burden, C. H. Chuang, et al., Mon. Not. R. Astron. Soc. 470, 2617 (2017).

    Article  ADS  Google Scholar 

  189. D. M. Scolnic, D. O. Jones, A. Rest, Y. C. Pan, R. Chornock, R. J. Foley, M. E. Huber, R. Kessler, G. Narayan, A. G. Riess, et al., Astrophys. J. 859, 101 (2018).

    Article  ADS  Google Scholar 

  190. D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, Publ. Astron. Soc. Pac. 125, 306 (2013).

    Article  ADS  Google Scholar 

  191. K. Liao, X. L. Fan, X. Ding, M. Biesiada, and Z. H. Zhu, Nat. Commun. 8, 1148 (2017), arXiv: 1703.04151.

    Article  ADS  Google Scholar 

  192. Z. J. Zhang, K. Yan, C. M. Li, G. Q. Zhang, and F. Y. Wang, Astrophys. J. 906, 49 (2021), arXiv: 2011.14494.

    Article  ADS  Google Scholar 

  193. M. Amiri, et al. (CHIME/FRB Collaboration), arXiv: 2502.11217.

  194. G. Y. Chen, and X. Li, Chin. Phys. C 48, 075102 (2024).

    Article  ADS  Google Scholar 

  195. T. C. Yang, T. Hashimoto, T. Y. Hsu, T. Goto, C. T. Ling, S. C. C. Ho, A. Y. A. Chen, and E. Kilerci, Astron. Astrophys. 693, A85 (2025), arXiv: 2411.02249.

    Article  Google Scholar 

  196. J.-F. Mo, W. Zhu, and L.-L. Feng, arXiv: 2502.05838.

  197. R. Reischke, and S. Hagstotz, Mon. Not. R. Astron. Soc. 524, 2237 (2023), arXiv: 2301.03527.

    Article  ADS  Google Scholar 

  198. R. Takahashi, J. Cosmol. Astropart. Phys. 2024(10), 057 (2024), arXiv: 2407.06621.

    Article  Google Scholar 

  199. J. N. Jahns-Schindler, L. G. Spitler, C. R. H. Walker, and C. M. Baugh, Mon. Not. R. Astron. Soc. 523, 5006 (2023), arXiv: 2306.00084.

    Article  ADS  Google Scholar 

  200. L. Marnoch, S. D. Ryder, C. W. James, A. C. Gordon, M. W. Sammons, J. X. Prochaska, N. Tejos, A. T. Deller, D. R. Scott, S. Bhandari, et al., Mon. Not. R. Astron. Soc. 525, 994 (2023), arXiv: 2307.14702.

    Article  ADS  Google Scholar 

  201. L. Connor, frb-grav-lensing (2022), gitHub repository, https://github.com/liamconnor/frb-grav-lensing.

    Google Scholar 

  202. M. Yue, X. Fan, J. Yang, and F. Wang, Astrophys. J. 925, 169 (2022), arXiv: 2112.02821.

    Article  ADS  Google Scholar 

  203. J. G. Zhang, Y. Li, J. M. Zou, Z. W. Zhao, J. F. Zhang, and X. Zhang, Universe 10, 207 (2024), arXiv: 2303.16775.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Liaoning Key Laboratory of Cosmology and Astrophysics & Department of Physics, College of Sciences, Northeastern University, Shenyang, 110819, China

    Ji-Guo Zhang, Yi-Fan Jiang, Ze-Wei Zhao, Jing-Zhao Qi, Jing-Fei Zhang & Xin Zhang

  2. Key Laboratory of Data Analytics and Optimization for Smart Industry (Ministry of Education), Northeastern University, Shenyang, 110819, China

    Xin Zhang

  3. National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Northeastern University, Shenyang, 110819, China

    Xin Zhang

Authors
  1. Ji-Guo Zhang
    View author publications

    Search author on:PubMed Google Scholar

  2. Yi-Fan Jiang
    View author publications

    Search author on:PubMed Google Scholar

  3. Ze-Wei Zhao
    View author publications

    Search author on:PubMed Google Scholar

  4. Jing-Zhao Qi
    View author publications

    Search author on:PubMed Google Scholar

  5. Jing-Fei Zhang
    View author publications

    Search author on:PubMed Google Scholar

  6. Xin Zhang
    View author publications

    Search author on:PubMed Google Scholar

Corresponding author

Correspondence to Xin Zhang.

Ethics declarations

Conflict of interest The authors declare that they have no conflict of interest.

Additional information

This work was supported by the National SKA Program of China (Grant Nos. 2022SKA0110200, and 2022SKA0110203), the National Natural Science Foundation of China (Grant Nos. 12473001, 11975072, 11835009, and 11875102), and the National 111 Project (Grant No. B16009). We are grateful to Wan-Peng Sun, Yichao Li, Tian-Nuo Li, Yun Chen, and Zheng-Xiang Li for helpful discussions. We thank Liam Connor for providing the frb-grav-lensing codebase [201], which facilitated the lensing probability calculations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, JG., Jiang, YF., Zhao, ZW. et al. Combining strongly lensed and unlensed fast radio bursts: To be a more precise late-universe probe. Sci. China Phys. Mech. Astron. 68, 280406 (2025). https://doi.org/10.1007/s11433-024-2647-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Version of record:

  • DOI: https://doi.org/10.1007/s11433-024-2647-2

Profiles

  1. Xin Zhang View author profile