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Testing the seesaw mechanism and leptogenesis with gravitational waves: Majorana versus Dirac cases

Anish Ghoshal1,*, Kazunori Kohri2,3,4,5,†, and Nimmala Narendra6,‡

  • *Contact author: anish.ghoshal@fuw.edu.pl
  • †Contact author: kazunori.kohri@gmail.com
  • ‡Contact author: nimmalanarendra@gmail.com
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Phys. Rev. D 113, 055050 – Published 30 March, 2026

DOI: https://doi.org/10.1103/zygj-4hhy

Abstract

We investigate the B−L gauge extension of the Standard Model that the Dirac seesaw mechanism with thermal leptogenesis leaves imprints in the early Universe via the stochastic gravitational background emanating from a network of cosmic strings when B−L symmetry is broken. With right-handed neutrino mass lighter than the typical scale of grand unification, the B−L symmetry protecting the right-handed neutrinos leads to constraints on the Yukawa couplings for both Dirac and Majorana scenarios. Estimating the predicted gravitational wave background we find that future space-borne missions could probe the range concerning thermal Dirac leptogenesis. In a comparative analysis between such probes of gravitational waves sourced from cosmic strings in Dirac and Majorana leptogenesis in the B−L extension, based on the energy scales of the leptogenesis, for instance, gravitational waves detectors will be able to probe the scale of Dirac leptogenesis up to 109  GeV, while for Majorana leptogenesis it would be upto 1012  GeV.

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References (158)

  1. Super-Kamiokande Collaboration, Constraints on neutrino oscillations using 1258 days of Super-Kamiokande solar neutrino data, Phys. Rev. Lett. 86, 5656 (2001).
  2. Super-Kamiokande Collaboration, Determination of solar neutrino oscillation parameters using 1496 days of Super-Kamiokande I data, Phys. Lett. B 539, 179 (2002).
  3. SNO Collaboration, Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory, Phys. Rev. Lett. 89, 011301 (2002).
  4. Super-Kamiokande Collaboration, A measurement of atmospheric neutrino oscillation parameters by Super-Kamiokande I, Phys. Rev. D 71, 112005 (2005).
  5. Super-Kamiokande Collaboration, Solar neutrino measurements in Super-Kamiokande-IV, Phys. Rev. D 94, 052010 (2016).
  6. Borexino Collaboration, Measurement of neutrino flux from the primary proton–proton fusion process in the Sun with Borexino detector, Phys. Part. Nucl. 47, 995 (2016).
  7. IceCube Collaboration, Measurement of atmospheric neutrino oscillations at 6–56 GeV with IceCube DeepCore, Phys. Rev. Lett. 120, 071801 (2018).
  8. ANTARES Collaboration, Measuring the atmospheric neutrino oscillation parameters and constraining the 3+1 neutrino model with ten years of ANTARES data, J. High Energy Phys. 06 (2019) 113.
  9. KamLAND Collaboration, Precision measurement of neutrino oscillation parameters with KamLAND, Phys. Rev. Lett. 100, 221803 (2008).
  10. T2K Collaboration, Indication of electron neutrino appearance from an accelerator-produced off-axis muon neutrino beam, Phys. Rev. Lett. 107, 041801 (2011).
  11. Double Chooz Collaboration, Indication of reactor ν¯e disappearance in the Double Chooz experiment, Phys. Rev. Lett. 108, 131801 (2012).
  12. T2K Collaboration, Observation of electron neutrino appearance in a muon neutrino beam, Phys. Rev. Lett. 112, 061802 (2014).
  13. KATRIN Collaboration, Direct neutrino-mass measurement with sub-electronvolt sensitivity, Nat. Phys. 18, 160 (2022).
  14. Planck Collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020).
  15. eBOSS Collaboration, Completed SDSS-IV extended baryon oscillation spectroscopic survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory, Phys. Rev. D 103, 083533 (2021).
  16. Particle Data Group, Review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
  17. B. D. Fields, K. A. Olive, T.-H. Yeh, and C. Young, Big-bang nucleosynthesis after Planck, J. Cosmol. Astropart. Phys. 03 (2020) 010.
  18. P. Minkowski, μ→eγ at a rate of one out of 109 Muon decays?, Phys. Lett. 67B, 421 (1977).
  19. T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131, 95 (1979).
  20. S. L. Glashow, The future of elementary particle physics, NATO Sci. Ser. B 61, 687 (1980).
  21. R. N. Mohapatra and G. Senjanovic, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44, 912 (1980).
  22. M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174, 45 (1986).
  23. S. Davidson and A. Ibarra, A lower bound on the right-handed neutrino mass from leptogenesis, Phys. Lett. B 535, 25 (2002).
  24. E. Nardi, Y. Nir, E. Roulet, and J. Racker, The importance of flavor in leptogenesis, J. High Energy Phys. 01 (2006) 164.
  25. A. Abada, S. Davidson, F.-X. Josse-Michaux, M. Losada, and A. Riotto, Flavor issues in leptogenesis, J. Cosmol. Astropart. Phys. 04 (2006) 004.
  26. A. Abada, S. Davidson, A. Ibarra, F. X. Josse-Michaux, M. Losada, and A. Riotto, Flavour matters in leptogenesis, J. High Energy Phys. 09 (2006) 010.
  27. G. F. Giudice, A. Notari, M. Raidal, A. Riotto, and A. Strumia, Towards a complete theory of thermal leptogenesis in the SM and MSSM, Nucl. Phys. B685, 89 (2004).
  28. V. Cirigliano et al., Neutrinoless double-beta decay: A roadmap for matching theory to experiment, arXiv:2203.12169.
  29. T. Endoh, S. Kaneko, S. K. Kang, T. Morozumi, and M. Tanimoto, CP violation in neutrino oscillation and leptogenesis, Phys. Rev. Lett. 89, 231601 (2002).
  30. P. Di Bari and A. Riotto, Successful type I leptogenesis with SO(10)-inspired mass relations, Phys. Lett. B 671, 462 (2009).
  31. E. Bertuzzo, P. Di Bari, and L. Marzola, The problem of the initial conditions in flavoured leptogenesis and the tauon N2-dominated scenario, Nucl. Phys. B849, 521 (2011).
  32. F. Buccella, D. Falcone, C. S. Fong, E. Nardi, and G. Ricciardi, Squeezing out predictions with leptogenesis from SO(10), Phys. Rev. D 86, 035012 (2012).
  33. G. Altarelli and D. Meloni, A non supersymmetric SO(10) grand unified model for all the physics below MGUT, J. High Energy Phys. 08 (2013) 021.
  34. C. S. Fong, D. Meloni, A. Meroni, and E. Nardi, Leptogenesis in SO(10), J. High Energy Phys. 01 (2015) 111.
  35. V. S. Mummidi and K. M. Patel, Leptogenesis and fermion mass fit in a renormalizable SO(10) model, J. High Energy Phys. 12 (2021) 042.
  36. K. M. Patel, Minimal spontaneous CP-violating GUT and predictions for leptonic CP phases, Phys. Rev. D 107, 075041 (2023).
  37. S. Ipek, A. D. Plascencia, and J. Turner, Assessing perturbativity and vacuum stability in high-scale leptogenesis, J. High Energy Phys. 12 (2018) 111.
  38. D. Croon, N. Fernandez, D. McKeen, and G. White, Stability, reheating and leptogenesis, J. High Energy Phys. 06 (2019) 098.
  39. LIGO Scientific and Virgo Collaborations, Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016).
  40. LIGO Scientific and Virgo Collaborations, GW151226: Observation of gravitational waves from a 22-solar-mass binary black hole coalescence, Phys. Rev. Lett. 116, 241103 (2016).
  41. C. L. Carilli and S. Rawlings, Science with the square kilometer array: Motivation, key science projects, standards and assumptions, New Astron. Rev. 48, 979 (2004).
  42. G. Janssen et al., Gravitational wave astronomy with the SKA, Proc. Sci. AASKA14 (2015) 037 [arXiv:1501.00127].
  43. A. Weltman et al., Fundamental physics with the square kilometre array, Publ. Astron. Soc. Aust. 37, e002 (2020).
  44. EPTA Collaboration, European Pulsar Timing Array limits on an isotropic stochastic gravitational-wave background, Mon. Not. R. Astron. Soc. 453, 2576 (2015).
  45. EPTA Collaboration, European Pulsar Timing Array limits on continuous gravitational waves from individual supermassive black hole binaries, Mon. Not. R. Astron. Soc. 455, 1665 (2016).
  46. NANOGrav Collaboration, The NANOGrav 15 yr data set: Evidence for a gravitational-wave background, Astrophys. J. Lett. 951, L8 (2023).
  47. NANOGrav Collaboration, The NANOGrav 15 yr data set: Search for signals from new physics, Astrophys. J. Lett. 951, L11 (2023).
  48. A. Ghoshal, D. Nanda, and A. K. Saha, CMB imprints of high scale non-thermal leptogenesis, Phys. Lett. B 849, 138484 (2024).
  49. J. A. Dror, T. Hiramatsu, K. Kohri, H. Murayama, and G. White, Testing the seesaw mechanism and leptogenesis with gravitational waves, Phys. Rev. Lett. 124, 041804 (2020).
  50. S. Saad, Probing minimal grand unification through gravitational waves, proton decay, and fermion masses, J. High Energy Phys. 04 (2023) 058.
  51. P. Di Bari, S. F. King, and M. H. Rahat, Gravitational waves from phase transitions and cosmic strings in neutrino mass models with multiple majorons, J. High Energy Phys. 05 (2024) 068.
  52. S. Blasi, V. Brdar, and K. Schmitz, Fingerprint of low-scale leptogenesis in the primordial gravitational-wave spectrum, Phys. Rev. Res. 2, 043321 (2020).
  53. B. Fu, A. Ghoshal, and S. F. King, Cosmic string gravitational waves from global U(1)B−L symmetry breaking as a probe of the type I seesaw scale, J. High Energy Phys. 11 (2023) 071.
  54. B. Barman, D. Borah, A. Dasgupta, and A. Ghoshal, Probing high scale Dirac leptogenesis via gravitational waves from domain walls, Phys. Rev. D 106, 015007 (2022).
  55. S. F. King, D. Marfatia, and M. H. Rahat, Toward distinguishing Dirac from Majorana neutrino mass with gravitational waves, Phys. Rev. D 109, 035014 (2024).
  56. A. Dasgupta, P. S. B. Dev, A. Ghoshal, and A. Mazumdar, Gravitational wave pathway to testable leptogenesis, Phys. Rev. D 106, 075027 (2022).
  57. D. Borah, A. Dasgupta, and I. Saha, Leptogenesis and dark matter through relativistic bubble walls with observable gravitational waves, J. High Energy Phys. 11 (2022) 136.
  58. D. K. Ghosh, A. Ghoshal, K. Mukherjee, N. Narendra, and N. Okada, Impact of non-thermal leptogenesis with early matter domination on gravitational waves from first-order phase transition, arXiv:2508.02619.
  59. A. Ghoshal, R. Samanta, and G. White, Bremsstrahlung high-frequency gravitational wave signatures of high-scale nonthermal leptogenesis, Phys. Rev. D 108, 035019 (2023).
  60. A. Datta and A. Sil, Probing leptogenesis through gravitational waves, arXiv:2410.01900.
  61. A. Datta, S. Khalil, R. K. Mandal, and A. Sil, Probing right handed neutrino assisted reheating with gravitational waves and leptogenesis, J. Cosmol. Astropart. Phys. 02 (2026) 061.
  62. M. Berbig and A. Ghoshal, Impact of high-scale seesaw and leptogenesis on inflationary tensor perturbations as detectable gravitational waves, J. High Energy Phys. 05 (2023) 172.
  63. Z. A. Borboruah, A. Ghoshal, and S. Ipek, Probing flavor violation and baryogenesis via primordial gravitational waves, J. High Energy Phys. 07 (2024) 228.
  64. A. Afzal and A. Ghoshal, Primordial black holes and scalar-induced gravitational waves in radiative hybrid inflation, Eur. Phys. J. C 84, 983 (2024).
  65. M. Chianese, G. Domènech, T. Papanikolaou, R. Samanta, and N. Saviano, Induced gravitational waves as cosmic tracers of leptogenesis, arXiv:2504.20135.
  66. Y. F. Perez-Gonzalez and J. Turner, Assessing the tension between a black hole dominated early universe and leptogenesis, Phys. Rev. D 104, 103021 (2021).
  67. S. Datta, A. Ghosal, and R. Samanta, Baryogenesis from ultralight primordial black holes and strong gravitational waves from cosmic strings, J. Cosmol. Astropart. Phys. 08 (2021) 021.
  68. S. Jyoti Das, D. Mahanta, and D. Borah, Low scale leptogenesis and dark matter in the presence of primordial black holes, J. Cosmol. Astropart. Phys. 11 (2021) 019.
  69. B. Barman, D. Borah, S. J. Das, and R. Roshan, Non-thermal origin of asymmetric dark matter from inflaton and primordial black holes, J. Cosmol. Astropart. Phys. 03 (2022) 031.
  70. N. Bernal, C. S. Fong, Y. F. Perez-Gonzalez, and J. Turner, Rescuing high-scale leptogenesis using primordial black holes, Phys. Rev. D 106, 035019 (2022).
  71. N. Bhaumik, A. Ghoshal, and M. Lewicki, Doubly peaked induced stochastic gravitational wave background: Testing baryogenesis from primordial black holes, J. High Energy Phys. 07 (2022) 130.
  72. N. Bhaumik, A. Ghoshal, R. K. Jain, and M. Lewicki, Distinct signatures of spinning PBH domination and evaporation: Doubly peaked gravitational waves, dark relics and CMB complementarity, J. High Energy Phys. 05 (2023) 169.
  73. A. Ghoshal, Y. F. Perez-Gonzalez, and J. Turner, Superradiant leptogenesis, J. High Energy Phys. 02 (2024) 113.
  74. Y. Cui and Z.-Z. Xianyu, Probing leptogenesis with the cosmological collider, Phys. Rev. Lett. 129, 111301 (2022).
  75. C. S. Fong, A. Ghoshal, A. Naskar, M. H. Rahat, and S. Saad, Primordial non-Gaussianity as a probe of seesaw and leptogenesis, J. High Energy Phys. 11 (2023) 182.
  76. R. Samanta and S. Datta, Gravitational wave complementarity and impact of NANOGrav data on gravitational leptogenesis, J. High Energy Phys. 05 (2021) 211.
  77. M. Chianese, S. Datta, G. Miele, R. Samanta, and N. Saviano, Probing flavored regimes of leptogenesis with gravitational waves from cosmic strings, Phys. Rev. D 111, L041305 (2025).
  78. A. Davidson, B−L as the fourth color within an SU(2)L×U(1)R×U(1) model, Phys. Rev. D 20, 776 (1979).
  79. R. E. Marshak and R. N. Mohapatra, Quark—lepton symmetry and B−L as the U(1) generator of the electroweak symmetry group, Phys. Lett. 91B, 222 (1980).
  80. W. Buchmüller, V. Domcke, K. Kamada, and K. Schmitz, The gravitational wave spectrum from cosmological B−L breaking, J. Cosmol. Astropart. Phys. 10 (2013) 003.
  81. W. Buchmuller, V. Domcke, H. Murayama, and K. Schmitz, Probing the scale of grand unification with gravitational waves, Phys. Lett. B 809, 135764 (2020).
  82. T. W. B. Kibble, Topology of cosmic domains and strings, J. Phys. A 9, 1387 (1976).
  83. M. B. Hindmarsh and T. W. B. Kibble, Cosmic strings, Rep. Prog. Phys. 58, 477 (1995).
  84. R. Jeannerot, J. Rocher, and M. Sakellariadou, How generic is cosmic string formation in SUSY GUTs, Phys. Rev. D 68, 103514 (2003).
  85. A. Vilenkin, Gravitational radiation from cosmic strings, Phys. Lett. 107B, 47 (1981).
  86. T. Vachaspati and A. Vilenkin, Gravitational radiation from cosmic strings, Phys. Rev. D 31, 3052 (1985).
  87. K. Dick, M. Lindner, M. Ratz, and D. Wright, Leptogenesis with Dirac neutrinos, Phys. Rev. Lett. 84, 4039 (2000).
  88. H. Murayama and A. Pierce, Realistic Dirac leptogenesis, Phys. Rev. Lett. 89, 271601 (2002).
  89. V. Domcke, K. Kamada, K. Mukaida, K. Schmitz, and M. Yamada, Wash-in leptogenesis, Phys. Rev. Lett. 126, 201802 (2021).
  90. V. Domcke, K. Kamada, K. Mukaida, K. Schmitz, and M. Yamada, Wash-in leptogenesis after axion inflation, J. High Energy Phys. 01 (2023) 053.
  91. A. Maleknejad, Chiral gravity waves and leptogenesis in inflationary models with non-Abelian gauge fields, Phys. Rev. D 90, 023542 (2014).
  92. A. Maleknejad, SU(2)R and its axion in cosmology: A common origin for inflation, cold sterile neutrinos, and baryogenesis, Phys. Rev. D 104, 083518 (2021).
  93. A. Maleknejad, Chiral anomaly in SU(2)R-axion inflation and the new prediction for particle cosmology, J. High Energy Phys. 06 (2021) 113.
  94. M. Boz and N. K. Pak, Dirac leptogenesis and anomalous U(1), Eur. Phys. J. C 37, 507 (2004).
  95. B. Thomas and M. Toharia, Phenomenology of Dirac neutrinogenesis in split supersymmetry, Phys. Rev. D 73, 063512 (2006).
  96. B. Thomas and M. Toharia, Lepton flavor violation and supersymmetric Dirac leptogenesis, Phys. Rev. D 75, 013013 (2007).
  97. D. G. Cerdeno, A. Dedes, and T. E. J. Underwood, The minimal phantom sector of the Standard Model: Higgs phenomenology and Dirac leptogenesis, J. High Energy Phys. 09 (2006) 067.
  98. P.-H. Gu and H.-J. He, Neutrino mass and baryon asymmetry from Dirac seesaw, J. Cosmol. Astropart. Phys. 12 (2006) 010.
  99. P.-H. Gu, H.-J. He, and U. Sarkar, Realistic neutrinogenesis with radiative vertex correction, Phys. Lett. B 659, 634 (2008).
  100. E. J. Chun and P. Roy, Dirac leptogenesis in extended nMSSM, J. High Energy Phys. 06 (2008) 089.
  101. A. Bechinger and G. Seidl, Resonant Dirac leptogenesis on throats, Phys. Rev. D 81, 065015 (2010).
  102. M.-C. Chen, J. Huang, and W. Shepherd, Dirac leptogenesis with a non-anomalous U(1)′ family symmetry, J. High Energy Phys. 11 (2012) 059.
  103. K.-Y. Choi, E. J. Chun, and C. S. Shin, Dark matter asymmetry in supersymmetric Dirac leptogenesis, Phys. Lett. B 723, 90 (2013).
  104. D. Borah and A. Dasgupta, Common origin of neutrino mass, dark matter and Dirac leptogenesis, J. Cosmol. Astropart. Phys. 12 (2016) 034.
  105. P.-H. Gu, Peccei-Quinn symmetry for Dirac seesaw and leptogenesis, J. Cosmol. Astropart. Phys. 07 (2016) 004.
  106. N. Narendra, N. Sahoo, and N. Sahu, Dark matter assisted Dirac leptogenesis and neutrino mass, Nucl. Phys. B936, 76 (2018).
  107. J. Heeck, Leptogenesis with lepton-number-violating Dirac neutrinos, Phys. Rev. D 88, 076004 (2013).
  108. P.-H. Gu, Leptogenesis with testable Dirac neutrino mass generation, Phys. Lett. B 805, 135411 (2020).
  109. D. Mahanta and D. Borah, Low scale Dirac leptogenesis and dark matter with observable ΔNeff, Eur. Phys. J. C 82, 495 (2022).
  110. E. Ma, Naturally small seesaw neutrino mass with no new physics beyond the TeV scale, Phys. Rev. Lett. 86, 2502 (2001).
  111. F. Wang, W. Wang, and J. M. Yang, Split two-Higgs-doublet model and neutrino condensation, Europhys. Lett. 76, 388 (2006).
  112. S. Gabriel and S. Nandi, A new two Higgs doublet model, Phys. Lett. B 655, 141 (2007).
  113. S. M. Davidson and H. E. Logan, Dirac neutrinos from a second Higgs doublet, Phys. Rev. D 80, 095008 (2009).
  114. S. M. Davidson and H. E. Logan, LHC phenomenology of a two-Higgs-doublet neutrino mass model, Phys. Rev. D 82, 115031 (2010).
  115. J. Heeck and W. Rodejohann, Neutrinoless quadruple beta decay, Europhys. Lett. 103, 32001 (2013).
  116. M.-C. Chen, M. Ratz, C. Staudt, and P. K. S. Vaudrevange, The mu term and neutrino masses, Nucl. Phys. B866, 157 (2013).
  117. D. Borah, D. Nanda, N. Narendra, and N. Sahu, Right-handed neutrino dark matter with radiative neutrino mass in gauged B−L model, Nucl. Phys. B950, 114841 (2020).
  118. C. Q. Geng and R. E. Marshak, Uniqueness of quark and lepton representations in the Standard Model from the anomalies viewpoint, Phys. Rev. D 39, 693 (1989).
  119. X. G. He, G. C. Joshi, and R. R. Volkas, Constraints from anomaly cancellation on strong, weak, and electromagnetic interactions, Phys. Rev. D 41, 278 (1990).
  120. K. Kohri and N. Sahu, Constraining the cogenesis of visible and dark matter with AMS-02 and Xenon-100, Phys. Rev. D 88, 103001 (2013).
  121. N. Narendra, S. Patra, N. Sahu, and S. Shil, Baryogenesis via leptogenesis from asymmetric dark matter and radiatively generated neutrino mass, Phys. Rev. D 98, 095016 (2018).
  122. E. J. Copeland and T. W. B. Kibble, Cosmic strings and superstrings, Proc. R. Soc. A 466, 623 (2010).
  123. J. Polchinski, Introduction to cosmic F- and D-strings, in NATO Advanced Study Institute and EC Summer School on String Theory: From Gauge Interactions to Cosmology (2004), pp. 229–253.
  124. Y. Gouttenoire, G. Servant, and P. Simakachorn, Beyond the Standard Models with cosmic strings, J. Cosmol. Astropart. Phys. 07 (2020) 032.
  125. L. M. A. Bettencourt, P. Laguna, and R. A. Matzner, Nonintercommuting cosmic strings, Phys. Rev. Lett. 78, 2066 (1997).
  126. A. Ghoshal, Y. Gouttenoire, L. Heurtier, and P. Simakachorn, Primordial black hole archaeology with gravitational waves from cosmic strings, J. High Energy Phys. 08 (2023) 196.
  127. A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, England, 2000).
  128. J. J. Blanco-Pillado, K. D. Olum, and B. Shlaer, The number of cosmic string loops, Phys. Rev. D 89, 023512 (2014).
  129. Particle Data Group, Review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
  130. 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).
  131. LIGO Scientific and Virgo Collaborations, GW170608: Observation of a 19-solar-mass binary black hole coalescence, Astrophys. J. Lett. 851, L35 (2017).
  132. LIGO Scientific and Virgo Collaborations, GW170814: A three-detector observation of gravitational waves from a binary black hole coalescence, Phys. Rev. Lett. 119, 141101 (2017).
  133. LIGO Scientific and Virgo Collaborations, GW170817: Observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119, 161101 (2017).
  134. LIGO Scientific Collaboration, Advanced LIGO, Classical Quantum Gravity 32, 074001 (2015).
  135. LIGO Scientific and Virgo Collaborations, Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo, SoftwareX 13, 100658 (2021).
  136. F. A. M. Punturo, M. Abernathy et al., The Einstein Telescope: A third-generation gravitational wave observatory, Classical Quantum Gravity 27, 194002 (2010).
  137. S. Hild et al., Sensitivity studies for third-generation gravitational wave observatories, Classical Quantum Gravity 28, 094013 (2011).
  138. D. Reitze et al., Cosmic Explorer: The U.S. contribution to gravitational-wave astronomy beyond LIGO, Bull. Am. Astron. Soc. 51, 035 (2019).
  139. A. Sesana et al., Unveiling the gravitational universe at μ-Hz frequencies, Exp. Astron. 51, 1333 (2021).
  140. P. Amaro-Seoane, H. Audley, S. B. et al., Laser Interferometer Space Antenna, arXiv:1702.00786.
  141. J. Baker et al., The Laser Interferometer Space Antenna: Unveiling the millihertz gravitational wave sky, arXiv:1907.06482.
  142. V. Corbin and N. J. Cornish, Detecting the cosmic gravitational wave background with the big bang observer, Classical Quantum Gravity 23, 2435 (2006).
  143. G. M. Harry, P. Fritschel, D. A. Shaddock, W. Folkner, and E. S. Phinney, Laser interferometry for the big bang observer, Classical Quantum Gravity 23, 4887 (2006).
  144. K. Yagi, N. Tanahashi, and T. Tanaka, Probing the size of extra dimension with gravitational wave astronomy, Phys. Rev. D 83, 084036 (2011).
  145. N. Seto, S. Kawamura, and T. Nakamura, Possibility of direct measurement of the acceleration of the universe using 0.1-Hz band laser interferometer gravitational wave antenna in space, Phys. Rev. Lett. 87, 221103 (2001).
  146. S. Kawamura, T. Nakamura, M. A. et al., The Japanese space gravitational wave antenna—DECIGO, Classical Quantum Gravity 23, S125 (2006).
  147. K. Yagi and N. Seto, Detector configuration of DECIGO/BBO and identification of cosmological neutron-star binaries, Phys. Rev. D 83, 044011 (2011).
  148. EPTA Collaboration, The European Pulsar Timing Array and the Large European Array for pulsars, Classical Quantum Gravity 30, 224009 (2013).
  149. EPTA Collaboration, European Pulsar Timing Array limits on an isotropic stochastic gravitational-wave background, Mon. Not. R. Astron. Soc. 453, 2576 (2015).
  150. EPTA Collaboration, European Pulsar Timing Array limits on continuous gravitational waves from individual supermassive black hole binaries, Mon. Not. R. Astron. Soc. 455, 1665 (2016).
  151. M. A. McLaughlin, The North American Nanohertz Observatory for gravitational waves, Classical Quantum Gravity 30, 224008 (2013).
  152. NANOGRAV Collaboration, The NANOGrav 11-year data set: Pulsar-timing constraints on the stochastic gravitational-wave background, Astrophys. J. 859, 47 (2018).
  153. K. Aggarwal et al., The NANOGrav 11-year data set: Limits on gravitational waves from individual supermassive black hole binaries, Astrophys. J. 880, 2 (2019).
  154. A. Brazier et al., The NANOGrav program for gravitational waves and fundamental physics, arXiv:1908.05356.
  155. NANOGrav Collaboration, The NANOGrav 12.5 yr data set: Search for an isotropic stochastic gravitational-wave background, Astrophys. J. Lett. 905, L34 (2020).
  156. J. Garcia-Bellido, H. Murayama, and G. White, Exploring the early Universe with Gaia and Theia, J. Cosmol. Astropart. Phys. 12 (2021) 023.
  157. E. Thrane and J. D. Romano, Sensitivity curves for searches for gravitational-wave backgrounds, Phys. Rev. D 88, 124032 (2013).
  158. C. Caprini et al., Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions, J. Cosmol. Astropart. Phys. 04 (2016) 001.

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Phys. Rev. D 113, 055050– Published 30 March, 2026
  • Received 10 September 2025
  • Accepted 5 February 2026
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