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Superheavy dark matter from the string theory axiverse

Siyang Ling1, Andrew J. Long2, Evan McDonough3, and Alex Hayes3,4

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Phys. Rev. D 112, 023550 – Published 29 July, 2025

DOI: https://doi.org/10.1103/wyc2-fytd

Abstract

We propose heavy axions as a natural superheavy dark matter candidate in string theory, with the relic density of dark matter originating in quantum fluctuations during cosmic inflation. String theory is well known for the possibility of having tens to hundreds of axionlike particles—the axiverse. Moduli stabilization generates high-scale masses for many of these, placing them naturally in the “superheavy” regime of particle physics. We consider moduli stabilization in the Kachru-Kallosh-Linde-Trivedi framework, featuring a single volume modulus and C4 axion, and a fiducial inflation model minimally coupled to the volume modulus. We demonstrate that both the volume modulus and the axion can be abundantly produced through gravitational particle production. The former is unstable and readily decays to Standard Model particles while the latter (the axion) can be stable and survives to constitute the present day dark matter.

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References (125)

  1. P. Svrcek and E. Witten, Axions in string theory, J. High Energy Phys. 06 (2006) 051.
  2. A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell, String axiverse, Phys. Rev. D 81, 123530 (2010).
  3. M. Cicoli, M. Goodsell, and A. Ringwald, The type IIB string axiverse and its low-energy phenomenology, J. High Energy Phys. 10 (2012) 146.
  4. R. D. Peccei and H. R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38, 1440 (1977).
  5. F. Wilczek, Problem of strong P and T invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
  6. S. Weinberg, A new light boson?, Phys. Rev. Lett. 40, 223 (1978).
  7. J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. 120B, 127 (1983).
  8. L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. 120B, 133 (1983).
  9. M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. 120B, 137 (1983).
  10. A. Maleknejad and E. McDonough, Ultralight pion and superheavy baryon dark matter, Phys. Rev. D 106, 095011 (2022).
  11. S. Alexander, H. Gilmer, T. Manton, and E. McDonough, π-axion and π-axiverse of dark QCD, Phys. Rev. D 108, 123014 (2023).
  12. S. Alexander, T. Manton, and E. McDonough, Field theory axiverse, Phys. Rev. D 109, 116019 (2024).
  13. I. Broeckel, M. Cicoli, A. Maharana, K. Singh, and K. Sinha, Moduli stabilisation and the statistics of axion physics in the landscape, J. High Energy Phys. 08 (2021) 059; 01 (2021) 191(A).
  14. J. Halverson, C. Long, B. Nelson, and G. Salinas, Towards string theory expectations for photon couplings to axionlike particles, Phys. Rev. D 100, 106010 (2019).
  15. V. M. Mehta, M. Demirtas, C. Long, D. J. E. Marsh, L. Mcallister, and M. J. Stott, Superradiance exclusions in the landscape of type IIB string theory, arXiv:2011.08693.
  16. V. M. Mehta, M. Demirtas, C. Long, D. J. E. Marsh, L. McAllister, and M. J. Stott, Superradiance in string theory, J. Cosmol. Astropart. Phys. 07 (2021) 033.
  17. M. Demirtas, N. Gendler, C. Long, L. McAllister, and J. Moritz, PQ axiverse, J. High Energy Phys. 06 (2023) 092.
  18. N. Gendler, D. J. E. Marsh, L. McAllister, and J. Moritz, Glimmers from the axiverse, J. Cosmol. Astropart. Phys. 09 (2024) 071.
  19. W. Hu, R. Barkana, and A. Gruzinov, Cold and fuzzy dark matter, Phys. Rev. Lett. 85, 1158 (2000).
  20. L. Hui, J. P. Ostriker, S. Tremaine, and E. Witten, Ultralight scalars as cosmological dark matter, Phys. Rev. D 95, 043541 (2017).
  21. M. Cicoli, V. Guidetti, N. Righi, and A. Westphal, Fuzzy dark matter candidates from string theory, J. High Energy Phys. 05 (2022) 107.
  22. J. Halverson, B. D. Nelson, F. Ruehle, and G. Salinas, Dark glueballs and their ultralight axions, Phys. Rev. D 98, 043502 (2018).
  23. T. Karwal and M. Kamionkowski, Dark energy at early times, the Hubble parameter, and the string axiverse, Phys. Rev. D 94, 103523 (2016).
  24. V. Poulin, T. L. Smith, T. Karwal, and M. Kamionkowski, Early dark energy can resolve the Hubble tension, Phys. Rev. Lett. 122, 221301 (2019).
  25. E. McDonough and M. Scalisi, Towards early dark energy in string theory, J. High Energy Phys. 10 (2023) 118.
  26. M. Cicoli, M. Licheri, R. Mahanta, E. McDonough, F. G. Pedro, and M. Scalisi, Early dark energy in type IIB string theory, J. High Energy Phys. 06 (2023) 052.
  27. D. Baumann and L. McAllister, Inflation and String Theory, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2015).
  28. E. W. Kolb, D. J. H. Chung, and A. Riotto, WIMPzillas!, AIP Conf. Proc. 484, 91 (1999).
  29. D. Carney et al., Snowmass2021 cosmic frontier white paper: Ultraheavy particle dark matter, SciPost Phys. Core 6, 075 (2023).
  30. K. Griest and M. Kamionkowski, Unitarity limits on the mass and radius of dark matter particles, Phys. Rev. Lett. 64, 615 (1990).
  31. L. Parker, Quantized fields and particle creation in expanding universes. I, Phys. Rev. 183, 1057 (1969).
  32. L. Parker, Quantized fields and particle creation in expanding universes. II, Phys. Rev. D 3, 346 (1971); 3, 2546(E) (1971).
  33. E. Schrödinger, The proper vibrations of the expanding universe, Physica (Utrecht) 6, 899 (1939).
  34. L. H. Ford, Cosmological particle production: A review, Rep. Prog. Phys. 84, 116901 (2021).
  35. E. W. Kolb and A. J. Long, Cosmological gravitational particle production and its implications for cosmological relics, Rev. Mod. Phys. 96, 045005 (2024).
  36. G. W. Gibbons and S. W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys. Rev. D 15, 2738 (1977).
  37. A. Lapedes, Bogolyubov transformations, propagators, and the Hawking effect, J. Math. Phys. (N.Y.) 19, 2289 (1978).
  38. A. Nakayama, Notes on the Hawking effect in de Sitter space. II, Phys. Rev. D 37, 354 (1988).
  39. W. H. Kinney, Cosmology, inflation, and the physics of nothing, NATO Sci. Ser. II 123, 189 (2003).
  40. V. Kuzmin and I. Tkachev, Ultrahigh-energy cosmic rays, superheavy long living particles, and matter creation after inflation, JETP Lett. 68, 271 (1998).
  41. D. J. H. Chung, E. W. Kolb, and A. Riotto, Superheavy dark matter, Phys. Rev. D 59, 023501 (1998).
  42. D. J. H. Chung, E. W. Kolb, and A. Riotto, Nonthermal supermassive dark matter, Phys. Rev. Lett. 81, 4048 (1998).
  43. D. J. H. Chung, E. W. Kolb, A. Riotto, and L. Senatore, Isocurvature constraints on gravitationally produced superheavy dark matter, Phys. Rev. D 72, 023511 (2005).
  44. P. W. Graham, J. Mardon, and S. Rajendran, Vector dark matter from inflationary fluctuations, Phys. Rev. D 93, 103520 (2016).
  45. M. Garny, M. Sandora, and M. S. Sloth, Planckian interacting massive particles as dark matter, Phys. Rev. Lett. 116, 101302 (2016).
  46. Y. Ema, R. Jinno, K. Mukaida, and K. Nakayama, Gravitational effects on inflaton decay, J. Cosmol. Astropart. Phys. 05 (2015) 038.
  47. Y. Ema, R. Jinno, K. Mukaida, and K. Nakayama, Gravitational particle production in oscillating backgrounds and its cosmological implications, Phys. Rev. D 94, 063517 (2016).
  48. M. Garny, A. Palessandro, M. Sandora, and M. S. Sloth, Theory and phenomenology of Planckian interacting massive particles as dark matter, J. Cosmol. Astropart. Phys. 02 (2018) 027.
  49. Y. Ema, K. Nakayama, and Y. Tang, Production of purely gravitational dark matter, J. High Energy Phys. 09 (2018) 135.
  50. M. Garny, A. Palessandro, M. Sandora, and M. S. Sloth, Charged Planckian interacting dark matter, J. Cosmol. Astropart. Phys. 01 (2019) 021.
  51. L. Li, T. Nakama, C. M. Sou, Y. Wang, and S. Zhou, Gravitational production of superheavy dark matter and associated cosmological signatures, J. High Energy Phys. 07 (2019) 067.
  52. Y. Ema, K. Nakayama, and Y. Tang, Production of purely gravitational dark matter: The case of fermion and vector boson, J. High Energy Phys. 07 (2019) 060.
  53. E. W. Kolb and A. J. Long, Completely dark photons from gravitational particle production during the inflationary era, J. High Energy Phys. 03 (2021) 283.
  54. A. Ahmed, B. Grzadkowski, and A. Socha, Gravitational production of vector dark matter, J. High Energy Phys. 08 (2020) 059.
  55. S. Alexander, L. Jenks, and E. McDonough, Higher spin dark matter, Phys. Lett. B 819, 136436 (2021).
  56. M. Redi, A. Tesi, and H. Tillim, Gravitational production of a conformal dark sector, J. High Energy Phys. 05 (2021) 010.
  57. S. Ling and A. J. Long, Superheavy scalar dark matter from gravitational particle production in α-attractor models of inflation, Phys. Rev. D 103, 103532 (2021).
  58. S. Clery, Y. Mambrini, K. A. Olive, and S. Verner, Gravitational portals in the early Universe, Phys. Rev. D 105, 075005 (2022).
  59. E. Dudas, M. A. G. Garcia, Y. Mambrini, K. A. Olive, M. Peloso, and S. Verner, Slow and safe gravitinos, Phys. Rev. D 103, 123519 (2021).
  60. E. W. Kolb, A. J. Long, and E. McDonough, Catastrophic production of slow gravitinos, Phys. Rev. D 104, 075015 (2021).
  61. E. W. Kolb, A. J. Long, and E. McDonough, Gravitino swampland conjecture, Phys. Rev. Lett. 127, 131603 (2021).
  62. Y. Mambrini and K. A. Olive, Gravitational production of dark matter during reheating, Phys. Rev. D 103, 115009 (2021).
  63. S. Clery, Y. Mambrini, K. A. Olive, A. Shkerin, and S. Verner, Gravitational portals with nonminimal couplings, Phys. Rev. D 105, 095042 (2022).
  64. E. Basso, D. J. H. Chung, E. W. Kolb, and A. J. Long, Quantum interference in gravitational particle production, J. High Energy Phys. 12 (2022) 108.
  65. O. Lebedev, T. Solomko, and J.-H. Yoon, Dark matter production via a non-minimal coupling to gravity, J. Cosmol. Astropart. Phys. 02 (2023) 035.
  66. O. Lebedev, Scalar overproduction in standard cosmology and predictivity of non-thermal dark matter, J. Cosmol. Astropart. Phys. 02 (2023) 032.
  67. O. Lebedev and J.-H. Yoon, On gravitational preheating, J. Cosmol. Astropart. Phys. 07 (2022) 001.
  68. S. Hashiba, S. Ling, and A. J. Long, An analytic evaluation of gravitational particle production of fermions via Stokes phenomenon, J. High Energy Phys. 09 (2022) 216.
  69. M. A. G. Garcia, M. Pierre, and S. Verner, Scalar dark matter production from preheating and structure formation constraints, Phys. Rev. D 107, 043530 (2023).
  70. K. Kaneta, S. M. Lee, and K.-y. Oda, Boltzmann or Bogoliubov? Approaches compared in gravitational particle production, J. Cosmol. Astropart. Phys. 09 (2022) 018.
  71. E. W. Kolb, A. J. Long, E. McDonough, and G. Payeur, Completely dark matter from rapid-turn multifield inflation, J. High Energy Phys. 02 (2023) 181.
  72. F. Koutroulis, O. Lebedev, and S. Pokorski, Gravitational production of sterile neutrinos, J. High Energy Phys. 04 (2024) 027.
  73. E. W. Kolb, S. Ling, A. J. Long, and R. A. Rosen, Cosmological gravitational particle production of massive spin-2 particles, J. High Energy Phys. 05 (2023) 181.
  74. C. Capanelli, L. Jenks, E. W. Kolb, and E. McDonough, Cosmological implications of Kalb-Ramond-like particles, J. High Energy Phys. 06 (2024) 075.
  75. K. Kaneta, W. Ke, Y. Mambrini, K. A. Olive, and S. Verner, Gravitational production of spin-3/2 particles during reheating, Phys. Rev. D 108, 115027 (2023).
  76. M. A. G. Garcia, M. Pierre, and S. Verner, New window into gravitationally produced scalar dark matter, Phys. Rev. D 108, 115024 (2023).
  77. M. A. G. Garcia, M. Pierre, and S. Verner, Isocurvature constraints on scalar dark matter production from the inflaton, Phys. Rev. D 107, 123508 (2023).
  78. M. A. G. Garcia, K. Kaneta, W. Ke, Y. Mambrini, K. A. Olive, and S. Verner, The role of vectors in reheating, J. Cosmol. Astropart. Phys. 06 (2024) 014.
  79. R. Zhang, Z. Xu, and S. Zheng, Gravitational freeze-in dark matter from Higgs preheating, J. Cosmol. Astropart. Phys. 07 (2023) 048.
  80. R. Zhang and S. Zheng, Gravitational dark matter from minimal preheating, J. High Energy Phys. 02 (2024) 061.
  81. D. Racco, S. Verner, and W. Xue, Gravitational production of heavy particles during and after inflation, J. High Energy Phys. 09 (2024) 129.
  82. G. Choi, M. A. G. Garcia, W. Ke, Y. Mambrini, K. A. Olive, and S. Verner, Inflaton production of scalar dark matter through fluctuations and scattering, Phys. Rev. D 110, 083512 (2024).
  83. C. Capanelli, L. Jenks, E. W. Kolb, and E. McDonough, Gravitational production of completely dark photons with nonminimal couplings to gravity, J. High Energy Phys. 09 (2024) 071.
  84. C. Capanelli, L. Jenks, E. W. Kolb, and E. McDonough, Runaway gravitational production of dark photons, Phys. Rev. Lett. 133, 061602 (2024).
  85. L. Jenks, E. W. Kolb, and K. Thyme, Gravitational particle production of scalars: Analytic and numerical approaches including early reheating, J. High Energy Phys. 05 (2025) 077.
  86. S. Verner, Nonminimal superheavy dark matter, J. Cosmol. Astropart. Phys. 05 (2025) 060.
  87. M. A. G. Garcia, W. Ke, Y. Mambrini, K. A. Olive, and S. Verner, Scalar field fluctuations and the production of dark matter, arXiv:2502.20471.
  88. D. Feiteira and O. Lebedev, Cosmological gravitational particle production: Starobinsky vs Bogolyubov, uncertainties, and issues, J. Cosmol. Astropart. Phys. 07 (2025) 003.
  89. R. Allahverdi, I. Broeckel, M. Cicoli, and J. K. Osiński, Superheavy dark matter from string theory, J. High Energy Phys. 02 (2021) 026.
  90. R. Allahverdi, C. Arina, M. Chianese, M. Cicoli, F. Maltoni, D. Massaro, and J. K. Osiński, Phenomenology of superheavy decaying dark matter from string theory, J. High Energy Phys. 02 (2024) 192.
  91. J. M. Leedom, M. Putti, N. Righi, and A. Westphal, Preheating axions in string cosmology, J. High Energy Phys. 04 (2025) 095.
  92. R. Kallosh and A. D. Linde, Landscape, the scale of SUSY breaking, and inflation, J. High Energy Phys. 12 (2004) 004.
  93. S. Alexander and N. Yunes, Chern-Simons modified general relativity, Phys. Rep. 480, 1 (2009).
  94. C. V. Johnson, D-brane primer, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 99): Strings, Branes, and Gravity (World Scientific Publishing, Singapore, 2000), pp. 129–350.
  95. M. Cicoli, A. Schachner, and P. Shukla, Systematics of type IIB moduli stabilisation with odd axions, J. High Energy Phys. 04 (2022) 003.
  96. S. Kachru, R. Kallosh, A. D. Linde, and S. P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68, 046005 (2003).
  97. V. Balasubramanian, P. Berglund, J. P. Conlon, and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, J. High Energy Phys. 03 (2005) 007.
  98. J. P. Conlon, F. Quevedo, and K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, J. High Energy Phys. 08 (2005) 007.
  99. M. Cicoli, J. P. Conlon, and F. Quevedo, General analysis of LARGE volume scenarios with string loop moduli stabilisation, J. High Energy Phys. 10 (2008) 105.
  100. K. Becker, M. Becker, M. Haack, and J. Louis, Supersymmetry breaking and alpha-prime corrections to flux induced potentials, J. High Energy Phys. 06 (2002) 060.
  101. S. B. Giddings, S. Kachru, and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66, 106006 (2002).
  102. C. P. Burgess and F. Quevedo, Axion homeopathy: Screening dilaton interactions, J. Cosmol. Astropart. Phys. 04 (2022) 007.
  103. C. P. Burgess, D. Dineen, and F. Quevedo, Yoga Dark Energy: Natural relaxation and other dark implications of a supersymmetric gravity sector, J. Cosmol. Astropart. Phys. 03 (2022) 064.
  104. P. Brax, C. P. Burgess, and F. Quevedo, Light axiodilatons: Matter couplings, weak-scale completions and long-distance tests of gravity, J. Cosmol. Astropart. Phys. 08 (2022) 011.
  105. P. Brax, C. P. Burgess, and F. Quevedo, Axio-Chameleons: A novel string-friendly multi-field screening mechanism, J. Cosmol. Astropart. Phys. 03 (2023) 015.
  106. S. Kachru, R. Kallosh, A. D. Linde, J. M. Maldacena, L. P. McAllister, and S. P. Trivedi, Towards inflation in string theory, J. Cosmol. Astropart. Phys. 10 (2003) 013.
  107. S. Ferrara, R. Kallosh, and A. Linde, Cosmology with nilpotent superfields, J. High Energy Phys. 10 (2014) 143.
  108. E. McDonough and M. Scalisi, Inflation from nilpotent Kähler corrections, J. Cosmol. Astropart. Phys. 11 (2016) 028.
  109. R. Kallosh, A. Linde, D. Roest, and Y. Yamada, D3¯ induced geometric inflation, J. High Energy Phys. 07 (2017) 057.
  110. M. Cicoli, K. Dutta, A. Maharana, and F. Quevedo, Moduli vacuum misalignment and precise predictions in string inflation, J. Cosmol. Astropart. Phys. 08 (2016) 006.
  111. C. Gordon, D. Wands, B. A. Bassett, and R. Maartens, Adiabatic and entropy perturbations from inflation, Phys. Rev. D 63, 023506 (2000).
  112. D. Wands, N. Bartolo, S. Matarrese, and A. Riotto, An observational test of two-field inflation, Phys. Rev. D 66, 043520 (2002).
  113. D. Langlois and S. Renaux-Petel, Perturbations in generalized multi-field inflation, J. Cosmol. Astropart. Phys. 04 (2008) 017.
  114. C. M. Peterson and M. Tegmark, Testing two-field inflation, Phys. Rev. D 83, 023522 (2011).
  115. J.-O. Gong and T. Tanaka, A covariant approach to general field space metric in multi-field inflation, J. Cosmol. Astropart. Phys. 03 (2011) 015; 02 (2012) E01(E).
  116. D. I. Kaiser, E. A. Mazenc, and E. I. Sfakianakis, Primordial bispectrum from multifield inflation with nonminimal couplings, Phys. Rev. D 87, 064004 (2013).
  117. J.-O. Gong, Multi-field inflation and cosmological perturbations, Int. J. Mod. Phys. D 26, 1740003 (2016).
  118. E. McDonough, A. H. Guth, and D. I. Kaiser, Nonminimal couplings and the forgotten field of axion inflation, arXiv:2010.04179.
  119. L. Parker, Particle creation in expanding universes, Phys. Rev. Lett. 21, 562 (1968).
  120. D. J. H. Chung, E. W. Kolb, and A. J. Long, Gravitational production of super-Hubble-mass particles: An analytic approach, J. High Energy Phys. 01 (2018) 189.
  121. S. Das, K. Murase, and T. Fujii, Revisiting ultrahigh-energy constraints on decaying superheavy dark matter, Phys. Rev. D 107, 103013 (2023).
  122. A. Alonzo-Artiles, A. Avilez-López, J. L. Díaz-Cruz, and B. O. Larios-López, The Higgs-graviton couplings: From amplitudes to the action, arXiv:2105.11684.
  123. Y. Ema, K. Mukaida, and K. Nakayama, Scalar field couplings to quadratic curvature and decay into gravitons, J. High Energy Phys. 05 (2021) 087.
  124. R. Blumenhagen, G. Honecker, and T. Weigand, Loop-corrected compactifications of the heterotic string with line bundles, J. High Energy Phys. 06 (2005) 020.
  125. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).

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Phys. Rev. D 112, 023550– Published 29 July, 2025
  • Received 30 April 2025
  • Accepted 6 July 2025
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