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Gravitational waves from postinflationary magnetism: Direct and scalar-induced contributions

Subhasis Maiti*

  • *Contact author: subhashish@iitg.ac.in
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Phys. Rev. D 114, 043530 – Published 17 August, 2026

DOI: https://doi.org/10.1103/8jkm-5l84

Abstract

We study stochastic gravitational waves (GWs) generated in a postinflationary magnetogenesis scenario with time-dependent gauge couplings during inflation and reheating. In this setup, magnetic anisotropic stress directly sources gravitational waves, while the induced curvature perturbations generate an additional scalar-induced GW component. We compare the spectral behavior of the two contributions and find that the magnetic-originated GW dominates the peak amplitude, whereas the scalar-induced contribution becomes important on larger scales. For nb≥3/2, both contributions exhibit the universal infrared scaling ΩGW(f<fpeak)∝f3, while their ultraviolet slopes differ, leading to distinct spectral signatures. For suitable reheating and magnetogenesis parameters, the resulting GW signal naturally extends into the nano-Hz range relevant for pulsar timing array observations, and it remains consistent with other bounds. The distinct spectral features of the two components may provide a useful probe of reheating dynamics and primordial magnetogenesis.

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References (152)

  1. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 116, 061102 (2016).
  2. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 116, 241102 (2016).
  3. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 116, 131103 (2016).
  4. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. D 93, 122003 (2016).
  5. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 118, 221101 (2017); 121, 129901(E) (2018).
  6. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 118, 121101 (2017); 119, 029901(E) (2017).
  7. Y. Akrami et al. (Planck Collaboration), Astron. Astrophys. 641, A10 (2020).
  8. P. A. R. Ade et al. (BICEP and Keck Collaborations), Phys. Rev. Lett. 127, 151301 (2021).
  9. P. A. R. Ade et al. (BICEP2 and Keck Array Collaborations), Phys. Rev. Lett. 121, 221301 (2018).
  10. T. J. Clarke, E. J. Copeland, and A. Moss, J. Cosmol. Astropart. Phys. 10 (2020) 002.
  11. Y. Watanabe and E. Komatsu, Phys. Rev. D 73, 123515 (2006).
  12. C. Caprini and D. G. Figueroa, Classical Quantum Gravity 35, 163001 (2018).
  13. V. Acquaviva, N. Bartolo, S. Matarrese, and A. Riotto, Nucl. Phys. B667, 119 (2003).
  14. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  15. I. Sendra and T. L. Smith, Phys. Rev. D 85, 123002 (2012).
  16. A. Afzal et al. (NANOGrav Collaboration), Astrophys. J. Lett. 951, L11 (2023); 971, L27(E) (2024).
  17. L. Sorbo, J. Cosmol. Astropart. Phys. 06 (2011) 003.
  18. C. Caprini and L. Sorbo, J. Cosmol. Astropart. Phys. 10 (2014) 056.
  19. A. Ito and J. Soda, Phys. Lett. B 771, 415 (2017).
  20. R. Sharma, K. Subramanian, and T. R. Seshadri, Phys. Rev. D 101, 103526 (2020).
  21. A. A. Starobinsky, JETP Lett. 30, 682 (1979).
  22. L. P. Grishchuk, Zh. Eksp. Teor. Fiz. 67, 825 (1974).
  23. M. C. Guzzetti, N. Bartolo, M. Liguori, and S. Matarrese, Riv. Nuovo Cimento 39, 399 (2016).
  24. M. R. Haque, D. Maity, T. Paul, and L. Sriramkumar, Phys. Rev. D 104, 063513 (2021).
  25. J. Adams, B. Cresswell, and R. Easther, Phys. Rev. D 64, 123514 (2001).
  26. H. Di and Y. Gong, J. Cosmol. Astropart. Phys. 07 (2018) 007.
  27. C. Fu, P. Wu, and H. Yu, Phys. Rev. D 101, 023529 (2020).
  28. H. V. Ragavendra, P. Saha, L. Sriramkumar, and J. Silk, Phys. Rev. D 103, 083510 (2021).
  29. N. Bhaumik and R. K. Jain, Phys. Rev. D 104, 023531 (2021).
  30. M. Solbi and K. Karami, J. Cosmol. Astropart. Phys. 08 (2021) 056.
  31. D. G. Figueroa, S. Raatikainen, S. Rasanen, and E. Tomberg, J. Cosmol. Astropart. Phys. 05 (2022) 027.
  32. G. Domènech, S. Pi, and M. Sasaki, J. Cosmol. Astropart. Phys. 08 (2020) 017.
  33. R.-g. Cai, S. Pi, and M. Sasaki, Phys. Rev. Lett. 122, 201101 (2019).
  34. S. Maiti, D. Maity, and R. Srikanth, Phys. Rev. D 112, 043535 (2025).
  35. S. Maiti, Phys. Rev. D 112, 043536 (2025).
  36. S. Maiti, D. Maity, and R. Srikanth, Phys. Rev. D 112, 063552 (2025).
  37. A. Chakraborty, S. Maiti, and D. Maity, Phys. Rev. D 111, 083505 (2025).
  38. A. Chakraborty, M. R. Haque, D. Maity, and R. Mondal, Phys. Rev. D 108, 023515 (2023).
  39. A. Hoory, J. Martin, A. Paul, and L. Sriramkumar, J. Cosmol. Astropart. Phys. 05 (2026) 080.
  40. R. Inui, S. Jaraba, S. Kuroyanagi, and S. Yokoyama, J. Cosmol. Astropart. Phys. 05 (2024) 082.
  41. K. T. Abe, R. Inui, Y. Tada, and S. Yokoyama, J. Cosmol. Astropart. Phys. 05 (2023) 044.
  42. S. Okano and T. Fujita, J. Cosmol. Astropart. Phys. 03 (2021) 026.
  43. A. Fletcher, ASP Conf. Ser. 438, 197 (2011).
  44. R. Beck, Astron. Astrophys. Rev. 24, 4 (2016).
  45. M. Haverkorn, J. C. Brown, B. M. Gaensler, and N. M. McClure-Griffiths, Astrophys. J. 680, 362 (2008).
  46. P. Kronberg, Q. Dufton, H. Li, and S. Colgate, Astrophys. J. 560, 178 (2001).
  47. A. Brandenburg and E. Ntormousi, Annu. Rev. Astron. Astrophys. 61, 561 (2023).
  48. M. S. Turner and L. M. Widrow, Phys. Rev. D 37, 2743 (1988).
  49. F. D. Mazzitelli and F. M. Spedalieri, Phys. Rev. D 52, 6694 (1995).
  50. G. Lambiase and A. R. Prasanna, Phys. Rev. D 70, 063502 (2004).
  51. K. Yanagihara, F. Uchida, T. Fujita, and S. Tsujikawa, Phys. Rev. D 110, 083506 (2024).
  52. C. Caprini and R. Durrer, Phys. Rev. D 65, 023517 (2001).
  53. S. Maiti and D. Maity, J. Cosmol. Astropart. Phys. 04 (2026) 020.
  54. T. Fujita and S. Yokoyama, J. Cosmol. Astropart. Phys. 09 (2013) 009.
  55. T. Fujita and R. Namba, Phys. Rev. D 94, 043523 (2016).
  56. P. Amaro-Seoane et al., GW Notes 6, 4 (2013).
  57. E. Barausse et al., Gen. Relativ. Gravit. 52, 81 (2020).
  58. C. Caprini et al., J. Cosmol. Astropart. Phys. 04 (2016) 001.
  59. J. Crowder and N. J. Cornish, Phys. Rev. D 72, 083005 (2005).
  60. V. Corbin and N. J. Cornish, Classical Quantum Gravity 23, 2435 (2006).
  61. J. Baker et al., Bull. Am. Astron. Soc. 51, 243 (2019).
  62. N. Seto, S. Kawamura, and T. Nakamura, Phys. Rev. Lett. 87, 221103 (2001).
  63. S. Kawamura et al., Classical Quantum Gravity 28, 094011 (2011).
  64. A. Suemasa, K. Nakagawa, and M. Musha, Proc. SPIE Int. Soc. Opt. Eng. 10563, 105632V (2017).
  65. G. Janssen et al., Proc. Sci. AASKA14 (2015) 037 [arXiv:1501.00127].
  66. G. Agazie et al. (NANOGrav Collaboration), Astrophys. J. Lett. 951, L8 (2023).
  67. J. Antoniadis et al., Astron. Astrophys. 678, A48 (2023).
  68. D. J. Reardon et al., Astrophys. J. Lett. 951, L6 (2023).
  69. A. Zic et al., Pub. Astron. Soc. Aust. 40, e049 (2023).
  70. H. Xu et al., Res. Astron. Astrophys. 23, 075024 (2023).
  71. J. Luo et al. (TianQin Collaboration), Classical Quantum Gravity 33, 035010 (2016).
  72. R. J. Z. Ferreira, R. K. Jain, and M. S. Sloth, J. Cosmol. Astropart. Phys. 10 (2013) 004.
  73. T. Kobayashi, J. Cosmol. Astropart. Phys. 05 (2014) 040.
  74. T. Kobayashi and M. S. Sloth, Phys. Rev. D 100, 023524 (2019).
  75. M. R. Haque, D. Maity, and S. Pal, Phys. Rev. D 103, 103540 (2021).
  76. D. Maity, S. Pal, and T. Paul, J. Cosmol. Astropart. Phys. 05 (2021) 045.
  77. S. Tripathy, D. Chowdhury, R. K. Jain, and L. Sriramkumar, Phys. Rev. D 105, 063519 (2022).
  78. Y. Li and L.-Y. Zhang, Mod. Phys. Lett. A 37, 2250069 (2022).
  79. A. Benevides, A. Dabholkar, and T. Kobayashi, J. High Energy Phys. 11 (2018) 039.
  80. T. Kobayashi and M. S. Sloth, Phys. Rev. D 100, 023524 (2019).
  81. H. J. Hortúa and L. Castañeda, Phys. Rev. D 90, 123520 (2014).
  82. L. Campanelli, Int. J. Mod. Phys. D 18, 1395 (2009).
  83. R. K. Jain, R. Durrer, and L. Hollenstein, J. Phys. Conf. Ser. 484, 012062 (2014).
  84. R. Sharma, K. Subramanian, and T. R. Seshadri, Phys. Rev. D 97, 083503 (2018).
  85. K. Bamba, S. D. Odintsov, T. Paul, and D. Maity, Phys. Dark Universe 36, 101025 (2022).
  86. R. Sharma, S. Jagannathan, T. R. Seshadri, and K. Subramanian, Phys. Rev. D 96, 083511 (2017).
  87. T. Papanikolaou, C. Tzerefos, S. Capozziello, and G. Lambiase, J. Cosmol. Astropart. Phys. 01 (2025) 051.
  88. L. Dai, M. Kamionkowski, and J. Wang, Phys. Rev. Lett. 113, 041302 (2014).
  89. K. Subramanian, Rep. Prog. Phys. 79, 076901 (2016).
  90. D. Paoletti, F. Finelli, and F. Paci, Mon. Not. R. Astron. Soc. 396, 523 (2009).
  91. P. A. R. Ade et al. (Planck Collaboration), Astron. Astrophys. 594, A19 (2016).
  92. A. Zucca, Y. Li, and L. Pogosian, Phys. Rev. D 95, 063506 (2017).
  93. D. Paoletti, J. Chluba, F. Finelli, and J. Rubiño-Martín, Mon. Not. R. Astron. Soc. 517, 3916 (2022).
  94. P. A. R. Ade et al. (BICEP2 and Keck Arrary Collaborations), Phys. Rev. D 96, 102003 (2017).
  95. V. A. Acciari et al. (MAGIC Collaboration), Astron. Astrophys. 670, A145 (2023).
  96. K. Takahashi, M. Mori, K. Ichiki, and S. Inoue, Astrophys. J. Lett. 744, L7 (2011).
  97. T. C. Arlen, V. V. Vassilev, T. Weisgarber, S. P. Wakely, and S. Y. Shafi, Astrophys. J. 796, 18 (2014).
  98. T. C. Arlen, V. V. Vassiliev, T. Weisgarber, S. P. Wakely, and S. Y. Shafi, Astrophys. J. 796, 18 (2014).
  99. A. M. Taylor, I. Vovk, and A. Neronov, Astron. Astrophys. 529, A144 (2011).
  100. A. Neronov and I. Vovk, Science 328, 73 (2010).
  101. M. S. Pshirkov, P. G. Tinyakov, and F. R. Urban, Phys. Rev. Lett. 116, 191302 (2016).
  102. K. Kamada and A. J. Long, Phys. Rev. D 94, 123509 (2016).
  103. K. Kamada and A. J. Long, Phys. Rev. D 94, 063501 (2016).
  104. T. Fujita and K. Kamada, Phys. Rev. D 93, 083520 (2016).
  105. K. Kamada, F. Uchida, and J. Yokoyama, J. Cosmol. Astropart. Phys. 04 (2021) 034.
  106. B. A. Bassett, S. Tsujikawa, and D. Wands, Rev. Mod. Phys. 78, 537 (2006).
  107. D. Wands, K. A. Malik, D. H. Lyth, and A. R. Liddle, Phys. Rev. D 62, 043527 (2000).
  108. D. Baumann, arXiv:0907.5424.
  109. K. A. Malik and D. Wands, Phys. Rep. 475, 1 (2009).
  110. C. Bonvin, C. Caprini, and R. Durrer, Phys. Rev. D 88, 083515 (2013).
  111. J. R. Shaw and A. Lewis, Phys. Rev. D 81, 043517 (2010).
  112. S. Saga, H. Tashiro, and S. Yokoyama, J. Cosmol. Astropart. Phys. 05 (2020) 039.
  113. S. Maiti and D. Maity, arXiv:2605.14044.
  114. G. Domènech and J. Tränkle, J. Cosmol. Astropart. Phys. 12 (2025) 017.
  115. G. Domènech, S. Pi, A. Wang, and J. Wang, J. Cosmol. Astropart. Phys. 08 (2024) 054.
  116. G. Domènech, Universe 7, 398 (2021).
  117. G. Domènech and M. Sasaki, Phys. Rev. D 103, 063531 (2021).
  118. G. Domènech, Int. J. Mod. Phys. D 29, 2050028 (2020).
  119. S. Balaji, G. Domènech, and G. Franciolini, J. Cosmol. Astropart. Phys. 10 (2023) 041.
  120. S. Balaji, G. Domenech, and J. Silk, J. Cosmol. Astropart. Phys. 09 (2022) 016.
  121. R. Inui, C. Joana, H. Motohashi, S. Pi, Y. Tada, and S. Yokoyama, J. Cosmol. Astropart. Phys. 03 (2025) 021.
  122. D. Baumann, P. J. Steinhardt, K. Takahashi, and K. Ichiki, Phys. Rev. D 76, 084019 (2007).
  123. H. V. Ragavendra, P. Saha, L. Sriramkumar, and J. Silk, Phys. Rev. D 103, 083510 (2021).
  124. H. V. Ragavendra and L. Sriramkumar, Galaxies 11, 34 (2023).
  125. E. Dimastrogiovanni, M. Fasiello, A. Malhotra, and G. Tasinato, J. Cosmol. Astropart. Phys. 01 (2023) 018.
  126. R.-G. Cai, S. Pi, and M. Sasaki, Phys. Rev. D 102, 083528 (2020).
  127. T. Papanikolaou, J. Cosmol. Astropart. Phys. 10 (2022) 089.
  128. S. Maity, N. Bhaumik, M. R. Haque, D. Maity, and L. Sriramkumar, J. Cosmol. Astropart. Phys. 01 (2025) 118.
  129. K. Kohri and T. Terada, Phys. Rev. D 97, 123532 (2018).
  130. K. Inomata, M. Kawasaki, K. Mukaida, Y. Tada, and T. T. Yanagida, Phys. Rev. D 95, 123510 (2017).
  131. S. Maiti, D. Maity, and L. Sriramkumar, arXiv:2401.01864.
  132. A. Bhaumik, T. Papanikolaou, and A. Ghoshal, J. Cosmol. Astropart. Phys. 08 (2025) 054.
  133. H. V. Ragavendra, G. Tasinato, and L. Sriramkumar, Phys. Rev. D 113, 103547 (2026).
  134. L. A. Boyle and P. J. Steinhardt, Phys. Rev. D 77, 063504 (2008).
  135. B. Atkins, D. Chowdhury, A. Marriott-Best, and G. Tasinato, Phys. Rev. D 112, 063534 (2025).
  136. T. Papanikolaou, V. Vennin, and D. Langlois, J. Cosmol. Astropart. Phys. 03 (2021) 053.
  137. M. Punturo et al., Classical Quantum Gravity 27, 194002 (2010).
  138. B. Sathyaprakash et al., Classical Quantum Gravity 29, 124013 (2012); B. Sathyaprakash30, 079501(E) (2013).
  139. T. J. Clarke, E. J. Copeland, and A. Moss, J. Cosmol. Astropart. Phys. 10 (2020) 002.
  140. M. Rajagopal and R. W. Romani, Astrophys. J. 446, 543 (1995).
  141. A. H. Jaffe and D. C. Backer, Astrophys. J. 583, 616 (2003).
  142. J. S. B. Wyithe and A. Loeb, Astrophys. J. 590, 691 (2003).
  143. M. Enoki and M. Nagashima, Prog. Theor. Phys. 117, 241 (2007).
  144. A. Sesana, A. Vecchio, and C. N. Colacino, Mon. Not. R. Astron. Soc. 390, 192 (2008).
  145. L. Z. Kelley, L. Blecha, L. Hernquist, A. Sesana, and S. R. Taylor, Mon. Not. R. Astron. Soc. 471, 4508 (2017).
  146. M. Benetti, L. L. Graef, and S. Vagnozzi, Phys. Rev. D 105, 043520 (2022).
  147. S. Vagnozzi, Mon. Not. R. Astron. Soc. 502, L11 (2021).
  148. S. Vagnozzi, J. High Energy Astrophys. 39, 81 (2023).
  149. Q.-H. Zhu, Z.-C. Zhao, S. Wang, and X. Zhang, Chin. Phys. C 48, 125105 (2024).
  150. A. Mitridate, D. Wright, R. von Eckardstein, T. Schröder, J. Nay, K. Olum, K. Schmitz, and T. Trickle, arXiv:2306.16377.
  151. J. A. Ellis, M. Vallisneri, S. R. Taylor, and P. T. Baker, ENTERPRISE: Enhanced Numerical Toolbox Enabling a Robust PulsaR Inference SuitE, Astrophysics Source Code Library, record ascl:1912.015 (2019), ascl:1912.015.
  152. W. G. Lamb, S. R. Taylor, and R. van Haasteren, Phys. Rev. D 108, 103019 (2023).

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Phys. Rev. D 114, 043530– Published 17 August, 2026
  • Received 3 June 2026
  • Accepted 29 July 2026
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