- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Spontaneous breaking of the Peccei-Quinn symmetry during warm inflation

João G. Rosa1,2,* and Luís B. Ventura3,2,4,†

  • *Contact author: jgrosa@uc.pt
  • †Contact author: lbventur@gmail.com
PDF

Phys. Rev. D 113, 063515 – Published 4 March, 2026

DOI: https://doi.org/10.1103/t4jl-nbt5

Abstract

We show that, for values of the axion decay constant parametrically close to the grand unified theory scale, the Peccei-Quinn phase transition may naturally occur during warm inflation. This results from interactions between the Peccei-Quinn scalar field and the ambient thermal bath, which is sustained by the inflaton field through dissipative effects. It is therefore possible for the axion field to appear as a dynamical degree of freedom only after observable cosmic microwave background scales have become superhorizon, thus avoiding the large-scale axion isocurvature perturbations that typically plague such models. This nevertheless yields a nearly scale-invariant spectrum of axion isocurvature perturbations on small scales, with a density contrast of up to a few percent, which may have a significant impact on the formation of gravitationally bound axion structures such as miniclusters.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (46)

  1. R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977).
  2. J. Preskill, M. B. Wise, and F. Wilczek, Phys. Lett. 120B, 127 (1983).
  3. M. Dine and W. Fischler, Phys. Lett. 120B, 137 (1983).
  4. A. D. Linde, Phys. Lett. B 259, 38 (1991).
  5. D. H. Lyth, Phys. Lett. B 236, 408 (1990).
  6. D. J. E. Marsh, D. Grin, R. Hlozek, and P. G. Ferreira, Phys. Rev. Lett. 113, 011801 (2014).
  7. D. J. E. Marsh, Phys. Rep. 643, 1 (2016).
  8. T. Higaki, K. S. Jeong, and F. Takahashi, Phys. Lett. B 734, 21 (2014).
  9. K. Nakayama and M. Takimoto, Phys. Lett. B 748, 108 (2015).
  10. K. Choi, E. J. Chun, S. H. Im, and K. S. Jeong, Phys. Lett. B 750, 26 (2015).
  11. K. Schmitz and T. T. Yanagida, Phys. Rev. D 98, 075003 (2018).
  12. P. Sikivie, Lect. Notes Phys. 741, 19 (2008).
  13. A. Berera, Phys. Rev. Lett. 75, 3218 (1995).
  14. M. Levy, J. G. Rosa, and L. B. Ventura, J. High Energy Phys. 12 (2021) 176.
  15. A. Berera and L. Z. Fang, Phys. Rev. Lett. 74, 1912 (1995).
  16. A. Berera, Nucl. Phys. B585, 666 (2000).
  17. A. Berera, I. G. Moss, and R. O. Ramos, Rep. Prog. Phys. 72, 026901 (2009).
  18. M. Bastero-Gil and A. Berera, Int. J. Mod. Phys. A 24, 2207 (2009).
  19. A. Berera, M. Gleiser, and R. O. Ramos, Phys. Rev. Lett. 83, 264 (1999).
  20. A. Berera and R. O. Ramos, Phys. Lett. B 567, 294 (2003).
  21. I. G. Moss and C. Xiong, arXiv:hep-ph/0603266.
  22. I. G. Moss and C. M. Graham, Phys. Rev. D 78, 123526 (2008).
  23. M. Bastero-Gil, A. Berera, and R. O. Ramos, J. Cosmol. Astropart. Phys. 09 (2011) 033.
  24. M. Bastero-Gil, A. Berera, R. O. Ramos, and J. G. Rosa, J. Cosmol. Astropart. Phys. 01 (2013) 016.
  25. A. N. Taylor and A. Berera, Phys. Rev. D 62, 083517 (2000).
  26. L. M. H. Hall, I. G. Moss, and A. Berera, Phys. Rev. D 69, 083525 (2004).
  27. C. Graham and I. G. Moss, J. Cosmol. Astropart. Phys. 07 (2009) 013.
  28. R. O. Ramos and L. A. da Silva, J. Cosmol. Astropart. Phys. 03 (2013) 032.
  29. M. Bastero-Gil, A. Berera, R. O. Ramos, and J. G. Rosa, Phys. Rev. Lett. 117, 151301 (2016).
  30. M. Fukugita and T. Yanagida, Phys. Lett. B 174, 45 (1986).
  31. J. G. Rosa and L. B. Ventura, Phys. Rev. Lett. 122, 161301 (2019).
  32. J. G. Rosa and L. B. Ventura, Phys. Lett. B 798, 134984 (2019).
  33. M. Quiros, arXiv:hep-ph/9901312.
  34. J. E. Kim, Phys. Rev. Lett. 43, 103 (1979).
  35. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B166, 493 (1980).
  36. M. Bastero-Gil, A. Berera, R. Brandenberger, I. G. Moss, R. O. Ramos, and J. G. Rosa, J. Cosmol. Astropart. Phys. 01 (2018) 002.
  37. T. Hiramatsu, Y. Miyamoto, and J. Yokoyama, J. Cosmol. Astropart. Phys. 03 (2015) 024.
  38. A. D. Linde, Contemp. Concepts Phys. 5, 1 (1990).
  39. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020).
  40. L. Dai and J. Miralda-Escudé, Astron. J. 159, 49 (2020).
  41. P. J. Steinhardt and M. S. Turner, Phys. Lett. 129B, 51 (1983).
  42. G. Lazarides, R. K. Schaefer, D. Seckel, and Q. Shafi, Nucl. Phys. B346, 193 (1990).
  43. M. Kawasaki, T. Moroi, and T. Yanagida, Phys. Lett. B 383, 313 (1996).
  44. O. Bertolami, C. Cosme, and J. G. Rosa, Phys. Lett. B 759, 1 (2016).
  45. P. Laguna and W. H. Zurek, Phys. Rev. D 58, 085021 (1998).
  46. S. Bartrum, A. Berera, and J. G. Rosa, Phys. Rev. D 91, 083540 (2015).

Outline

Information

Phys. Rev. D 113, 063515– Published 4 March, 2026
  • Received 24 May 2021
  • Accepted 24 December 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation