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  • Letter
  • Open Access

No warm inflation from a vanilla axion

Sebastian Zell*

  • *Contact author: sebastian.zell@lmu.de
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Phys. Rev. D 112, L081307 – Published 17 October, 2025

DOI: https://doi.org/10.1103/kp15-3s1c

Abstract

At finite temperature, the coupling of an axion to non-Abelian gauge fields causes dissipation due to sphaleron heating. This mechanism has been considered as ideal for realizing warm inflation, since it can lead to large thermal friction while preserving the flatness of the potential. We show, however, that requiring standard properties of an axion—in particular, a discrete shift symmetry—excludes the strong regime of warm slow-roll inflation, in which thermal friction dominates. The present argument, which does not rely on any phenomenological input, leaves room for the weak regime of warm axion inflation, but in this case a super-Planckian decay constant represents a well-known issue. Finally, we discuss nonminimal and axionlike models as a way out.

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References (118)

  1. A. A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. 91B, 99 (1980).
  2. A. H. Guth, The inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D 23, 347 (1981).
  3. A. D. Linde, A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, Phys. Lett. 108B, 389 (1982).
  4. V. F. Mukhanov and G. V. Chibisov, Quantum fluctuations and a nonsingular universe, JETP Lett. 33, 532 (1981), http://jetpletters.ru/ps/1510/article_23079.pdf.
  5. Y. Akrami et al. (Planck Collaboration), Planck 2018 results. X. Constraints on inflation, Astron. Astrophys. 641, A10 (2020).
  6. P. A. R. Ade et al. (BICEP, Keck Collaborations), Improved constraints on primordial gravitational waves using Planck, WMAP, and BICEP/Keck observations through the 2018 observing season, Phys. Rev. Lett. 127, 151301 (2021).
  7. A. Riotto, Inflation and the theory of cosmological perturbations, ICTP Lect. Notes Ser. 14, 317 (2003), arXiv:hep-ph/0210162.
  8. V. Mukhanov, Physical Foundations of Cosmology (Cambridge University Press, Oxford, 2005).
  9. D. S. Gorbunov and V. A. Rubakov, Introduction to the Theory of the Early Universe: Cosmological Perturbations and Inflationary Theory (World Scientific, Singapore, 2011).
  10. D. Baumann, Cosmology (Cambridge University Press, Cambridge, England, 2022).
  11. E. J. Copeland, A. R. Liddle, D. H. Lyth, E. D. Stewart, and D. Wands, False vacuum inflation with Einstein gravity, Phys. Rev. D 49, 6410 (1994).
  12. P. Binetruy and G. R. Dvali, D term inflation, Phys. Lett. B 388, 241 (1996).
  13. G. R. Dvali and S. H. H. Tye, Brane inflation, Phys. Lett. B 450, 72 (1999).
  14. N. Arkani-Hamed, H.-C. Cheng, P. Creminelli, and L. Randall, Pseudonatural inflation, J. Cosmol. Astropart. Phys. 07 (2003) 003.
  15. D. Baumann and L. McAllister, Inflation and String Theory, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2015).
  16. A. Berera and L.-Z. Fang, Thermally induced density perturbations in the inflation era, Phys. Rev. Lett. 74, 1912 (1995).
  17. A. Berera, Warm inflation, Phys. Rev. Lett. 75, 3218 (1995).
  18. J. Yokoyama and A. D. Linde, Is warm inflation possible?, Phys. Rev. D 60, 083509 (1999).
  19. K. Freese, J. A. Frieman, and A. V. Olinto, Natural inflation with pseudo—Nambu-Goldstone bosons, Phys. Rev. Lett. 65, 3233 (1990).
  20. V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov, On the anomalous electroweak baryon number nonconservation in the early universe, Phys. Lett. 155B, 36 (1985).
  21. L. D. McLerran, E. Mottola, and M. E. Shaposhnikov, Sphalerons and axion dynamics in high temperature QCD, Phys. Rev. D 43, 2027 (1991).
  22. K. V. Berghaus, P. W. Graham, and D. E. Kaplan, Minimal warm inflation, J. Cosmol. Astropart. Phys. 03 (2020) 034; 10 (2023) E02.
  23. M. Laine and S. Procacci, Minimal warm inflation with complete medium response, J. Cosmol. Astropart. Phys. 06 (2021) 031.
  24. M. Mirbabayi and A. Gruzinov, Shapes of non-Gaussianity in warm inflation, J. Cosmol. Astropart. Phys. 02 (2022) 012.
  25. P. Klose, M. Laine, and S. Procacci, Gravitational wave background from vacuum and thermal fluctuations during axion-like inflation, J. Cosmol. Astropart. Phys. 12 (2022) 020.
  26. H. Kolesova, M. Laine, and S. Procacci, Maximal temperature of strongly-coupled dark sectors, J. High Energy Phys. 05 (2023) 239.
  27. P. Klose, M. Laine, and S. Procacci, Gravitational wave background from non-Abelian reheating after axion-like inflation, J. Cosmol. Astropart. Phys. 05 (2022) 021.
  28. M. Drewes and S. Zell, On sphaleron heating in the presence of fermions, J. Cosmol. Astropart. Phys. 06 (2023) 038.
  29. K. V. Berghaus, M. Forslund, and M. V. Guevarra, Minimal warm inflation with a heavy QCD axion, J. Cosmol. Astropart. Phys. 10 (2024) 103.
  30. V. Kamali, M. Motaharfar, and R. O. Ramos, Recent developments in warm inflation, Universe 9, 124 (2023).
  31. A. Berera, The warm inflation story, Universe 9, 272 (2023).
  32. R. D. Peccei and H. R. Quinn, Constraints imposed by CP conservation in the presence of instantons, Phys. Rev. D 16, 1791 (1977).
  33. R. D. Peccei and H. R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38, 1440 (1977).
  34. F. Wilczek, Problem of strong P and T invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
  35. S. Weinberg, A new light boson?, Phys. Rev. Lett. 40, 223 (1978).
  36. L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli, The landscape of QCD axion models, Phys. Rep. 870, 1 (2020).
  37. C. G. Callan, Jr., R. F. Dashen, and D. J. Gross, The structure of the gauge theory vacuum, Phys. Lett. B 63, 334 (1976).
  38. R. Jackiw and C. Rebbi, Vacuum periodicity in a Yang-Mills quantum theory, Phys. Rev. Lett. 37, 172 (1976).
  39. P. B. Arnold, D. Son, and L. G. Yaffe, The hot baryon violation rate is O(αw5T4), Phys. Rev. D 55, 6264 (1997).
  40. G. D. Moore and M. Tassler, The sphaleron rate in SU(N) gauge theory, J. High Energy Phys. 02 (2010) 105.
  41. M. Laine, L. Niemi, S. Procacci, and K. Rummukainen, Shape of the hot topological charge density spectral function, J. High Energy Phys. 11 (2022) 126.
  42. G. Buldgen, M. Drewes, J. U. Kang, and U. R. Mun, General Markovian equation for scalar fields in a slowly evolving background, J. Cosmol. Astropart. Phys. 05 (2019) 039.
  43. K. Kainulainen and O. Koskivaara, Non-equilibrium dynamics of a scalar field with quantum backreaction, J. High Energy Phys. 12 (2021) 190.
  44. J. E. Kim, Weak interaction singlet and strong CP invariance, Phys. Rev. Lett. 43, 103 (1979).
  45. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Can confinement ensure natural CP invariance of strong interactions?, Nucl. Phys. B166, 493 (1980).
  46. A. R. Zhitnitsky, On possible suppression of the axion hadron interactions. (In Russian), Sov. J. Nucl. Phys. 31, 260 (1980).
  47. M. Dine, W. Fischler, and M. Srednicki, A simple solution to the strong CP problem with a harmless axion, Phys. Lett. 104B, 199 (1981).
  48. D. J. E. Marsh, Axion cosmology, Phys. Rep. 643, 1 (2016).
  49. G. Grilli di Cortona, E. Hardy, J. Pardo Vega, and G. Villadoro, The QCD axion, precisely, J. High Energy Phys. 01 (2015) 034.
  50. K. V. Berghaus, P. W. Graham, D. E. Kaplan, G. D. Moore, and S. Rajendran, Dark energy radiation, Phys. Rev. D 104, 083520 (2021).
  51. S. H. H. Tye, A superstrong force with a heavy axion, Phys. Rev. Lett. 47, 1035 (1981).
  52. V. A. Rubakov, Grand unification and heavy axion, JETP Lett. 65, 621 (1997).
  53. Z. Berezhiani, L. Gianfagna, and M. Giannotti, Strong CP problem and mirror world: The Weinberg-Wilczek axion revisited, Phys. Lett. B 500, 286 (2001).
  54. A. Hook, Anomalous solutions to the strong CP problem, Phys. Rev. Lett. 114, 141801 (2015).
  55. H. Fukuda, K. Harigaya, M. Ibe, and T. T. Yanagida, Model of visible QCD axion, Phys. Rev. D 92, 015021 (2015).
  56. S. Dimopoulos, A. Hook, J. Huang, and G. Marques-Tavares, A collider observable QCD axion, J. High Energy Phys. 11 (2016) 052.
  57. A. Hook, S. Kumar, Z. Liu, and R. Sundrum, High quality QCD axion and the LHC, Phys. Rev. Lett. 124, 221801 (2020).
  58. A. Valenti, L. Vecchi, and L.-X. Xu, Grand color axion, J. High Energy Phys. 10 (2022) 025.
  59. R. T. Co, S. Kumar, and Z. Liu, Searches for heavy QCD axions via dimuon final states, J. High Energy Phys. 02 (2023) 111.
  60. D. I. Dunsky, L. J. Hall, and K. Harigaya, A heavy QCD axion and the mirror world, J. High Energy Phys. 02 (2023) 212.
  61. S. Mohanty and A. Nautiyal, Natural inflation at the GUT scale, Phys. Rev. D 78, 123515 (2008).
  62. H. Mishra, S. Mohanty, and A. Nautiyal, Warm natural inflation, Phys. Lett. B 710, 245 (2012).
  63. L. Visinelli, Natural warm inflation, J. Cosmol. Astropart. Phys. 09 (2011) 013.
  64. R. Z. Ferreira and A. Notari, Thermalized axion inflation, J. Cosmol. Astropart. Phys. 09 (2017) 007.
  65. R. Z. Ferreira and A. Notari, Thermalized axion inflation: Natural and monomial inflation with small r, Phys. Rev. D 97, 063528 (2018).
  66. V. Kamali, Warm pseudoscalar inflation, Phys. Rev. D 100, 043520 (2019).
  67. G. Montefalcone, V. Aragam, L. Visinelli, and K. Freese, Observational constraints on warm natural inflation, J. Cosmol. Astropart. Phys. 03 (2022) 002.
  68. A. D. Linde, Axions in inflationary cosmology, Phys. Lett. B 259, 38 (1991).
  69. A. D. Linde, Hybrid inflation, Phys. Rev. D 49, 748 (1994).
  70. M. Kamionkowski and J. March-Russell, Planck scale physics and the Peccei-Quinn mechanism, Phys. Lett. B 282, 137 (1992).
  71. J. Alvey and M. Escudero, The axion quality problem: Global symmetry breaking and wormholes, J. High Energy Phys. 01 (2021) 032; 11 (2023) 223(E).
  72. P. G. Catinari and A. Urbano, Gravitational instantons and the quality problem of the QCD axion: Facts, speculations, and statements in between, Phys. Rev. D 111, 125007 (2025).
  73. F. Takahashi and M. Yamada, Strongly broken Peccei-Quinn symmetry in the early universe, J. Cosmol. Astropart. Phys. 10 (2015) 010.
  74. M. Berbig, Minimal solution to the axion isocurvature problem from nonminimal coupling, Phys. Rev. D 110, 095008 (2024).
  75. C. Germani and T. Prokopec, On primordial black holes from an inflection point, Phys. Dark Universe 18, 6 (2017).
  76. A. Poisson, I. Timiryasov, and S. Zell, Critical points in Palatini Higgs inflation with small non-minimal coupling, J. High Energy Phys. 03 (2023) 130.
  77. S. Biswas, K. Bhattacharya, and S. Das, Embedding ultraslow-roll inflaton dynamics in warm inflation, Phys. Rev. D 109, 023501 (2024).
  78. Y. Reyimuaji and X. Zhang, Warm-assisted natural inflation, J. Cosmol. Astropart. Phys. 04 (2020) 077.
  79. M. Correa, M. R. Gangopadhyay, N. Jaman, and G. J. Mathews, Primordial black-hole dark matter via warm natural inflation, Phys. Lett. B 835, 137510 (2022).
  80. T. Higaki, K. S. Jeong, and F. Takahashi, Solving the tension between high-scale inflation and axion isocurvature perturbations, Phys. Lett. B 734, 21 (2014).
  81. K. Choi, K. S. Jeong, and M.-S. Seo, String theoretic QCD axions in the light of PLANCK and BICEP2, J. High Energy Phys. 07 (2014) 092.
  82. E. J. Chun, Axion dark matter with high-scale inflation, Phys. Lett. B 735, 164 (2014).
  83. M. Fairbairn, R. Hogan, and D. J. E. Marsh, Unifying inflation and dark matter with the Peccei-Quinn field: Observable axions and observable tensors, Phys. Rev. D 91, 023509 (2015).
  84. G. Ballesteros, J. Redondo, A. Ringwald, and C. Tamarit, Standard Model—axion—seesaw—Higgs portal inflation. Five problems of particle physics and cosmology solved in one stroke, J. Cosmol. Astropart. Phys. 08 (2017) 001.
  85. C. Rigouzzo and S. Zell, No dark matter axion during minimal Higgs inflation, arXiv:2504.02952.
  86. G. Ballesteros, A. Perez Rodriguez, and M. Pierre, Monomial warm inflation revisited, J. Cosmol. Astropart. Phys. 03 (2023) 003.
  87. G. K. Karananas, M. Shaposhnikov, and S. Zell, Weyl-invariant Einstein-Cartan gravity: Unifying the strong CP and hierarchy puzzles, J. High Energy Phys. 11 (2024) 146.
  88. S. Gupta, A. Berera, A. F. Heavens, and S. Matarrese, Non-Gaussian signatures in the cosmic background radiation from warm inflation, Phys. Rev. D 66, 043510 (2002).
  89. L. M. H. Hall, I. G. Moss, and A. Berera, Scalar perturbation spectra from warm inflation, Phys. Rev. D 69, 083525 (2004).
  90. S. Gupta, Dynamics and non-Gaussianity in the weak-dissipative warm inflation scenario, Phys. Rev. D 73, 083514 (2006).
  91. I. G. Moss and C. Xiong, Non-Gaussianity in fluctuations from warm inflation, J. Cosmol. Astropart. Phys. 04 (2007) 007.
  92. C. Graham and I. G. Moss, Density fluctuations from warm inflation, J. Cosmol. Astropart. Phys. 07 (2009) 013.
  93. I. G. Moss and T. Yeomans, Non-gaussianity in the strong regime of warm inflation, J. Cosmol. Astropart. Phys. 08 (2011) 009.
  94. M. Bastero-Gil, A. Berera, and R. O. Ramos, Shear viscous effects on the primordial power spectrum from warm inflation, J. Cosmol. Astropart. Phys. 07 (2011) 030.
  95. D. Lopez Nacir, R. A. Porto, L. Senatore, and M. Zaldarriaga, Dissipative effects in the effective field theory of inflation, J. High Energy Phys. 01 (2011) 075.
  96. R. O. Ramos and L. A. da Silva, Power spectrum for inflation models with quantum and thermal noises, J. Cosmol. Astropart. Phys. 03 (2013) 032.
  97. M. Bastero-Gil, A. Berera, I. G. Moss, and R. O. Ramos, Cosmological fluctuations of a random field and radiation fluid, J. Cosmol. Astropart. Phys. 05 (2014) 004.
  98. M. Bastero-Gil, A. Berera, I. G. Moss, and R. O. Ramos, Theory of non-Gaussianity in warm inflation, J. Cosmol. Astropart. Phys. 12 (2014) 008.
  99. M. Bastero-Gil, A. Berera, and J. R. Calderón, Reexamination of the warm inflation curvature perturbations spectrum, J. Cosmol. Astropart. Phys. 07 (2019) 019.
  100. S. Das and R. O. Ramos, Runaway potentials in warm inflation satisfying the Swampland conjectures, Phys. Rev. D 102, 103522 (2020).
  101. Y. Qiu and L. Sorbo, Spectrum of tensor perturbations in warm inflation, Phys. Rev. D 104, 083542 (2021).
  102. M. Bastero-Gil, J. M. Gomes, and J. a. G. Rosa, Thermal curvature perturbations in thermal inflation, J. Cosmol. Astropart. Phys. 06 (2023) 060.
  103. G. Montefalcone, V. Aragam, L. Visinelli, and K. Freese, WarmSPy: A numerical study of cosmological perturbations in warm inflation, J. Cosmol. Astropart. Phys. 01 (2023) 032.
  104. M. Drewes, Y. Georis, J. Klaric, and P. Klose, Upper bound on thermal gravitational wave backgrounds from hidden sectors, J. Cosmol. Astropart. Phys. 06 (2023) 073.
  105. M. Laine, S. Procacci, and A. Rogelj, Evolution of coupled scalar perturbations through smooth reheating. I. Dissipative regime, J. Cosmol. Astropart. Phys. 10 (2024) 040.
  106. N. Arkani-Hamed, H.-C. Cheng, P. Creminelli, and L. Randall, Extra natural inflation, Phys. Rev. Lett. 90, 221302 (2003).
  107. T. Banks, M. Dine, P. J. Fox, and E. Gorbatov, On the possibility of large axion decay constants, J. Cosmol. Astropart. Phys. 06 (2003) 001.
  108. J. E. Kim, H. P. Nilles, and M. Peloso, Completing natural inflation, J. Cosmol. Astropart. Phys. 01 (2005) 005.
  109. S. Dimopoulos, S. Kachru, J. McGreevy, and J. G. Wacker, N-flation, J. Cosmol. Astropart. Phys. 08 (2005) 003.
  110. E. Silverstein and A. Westphal, Monodromy in the CMB: Gravity waves and string inflation, Phys. Rev. D 78, 106003 (2008).
  111. L. McAllister, E. Silverstein, and A. Westphal, Gravity waves and linear inflation from axion monodromy, Phys. Rev. D 82, 046003 (2010).
  112. K. V. Berghaus and T. Karwal, Thermal friction as a solution to the Hubble tension, Phys. Rev. D 101, 083537 (2020).
  113. A. Papageorgiou, P. Quílez, and K. Schmitz, Axion dark matter from frictional misalignment, J. High Energy Phys. 01 (2022) 169.
  114. K. Choi, S. H. Im, H. J. Kim, and H. Seong, Axion dark matter with thermal friction, J. High Energy Phys. 02 (2022) 180.
  115. S. Biondini, H. Kolesova, and S. Procacci, Smooth reheating and dark matter via non-Abelian gauge theory, Phys. Lett. B 857, 138995 (2024).
  116. D. McKeen, R. Mizuta, D. E. Morrissey, and M. Shamma, Dark matter from dark glueball dominance, Phys. Rev. D 111, 015044 (2025).
  117. K. Freese, G. Montefalcone, and B. Shams Es Haghi, Dark matter production during warm inflation via freeze-in, Phys. Rev. Lett. 133, 211001 (2024).
  118. K. V. Berghaus, M. Drewes, and S. Zell, Warm inflation with the standard model, arXiv:2503.18829.

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Phys. Rev. D 112, L081307– Published 17 October, 2025
  • Received 18 October 2024
  • Accepted 24 September 2025
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