- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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

Cosmological Magnetic Fields from Ultralight Dark Matter

Robert Brandenberger1,*, Jürg Fröhlich2,†, and Hao Jiao1,3,‡

  • 1Department of Physics, McGill University, Montréal, Quebec H3A 2T8, Canada
  • 2Institute of Theoretical Physics, ETH Zürich, CH-8093 Zürich, Switzerland
  • 3Cosmology, Gravity and Astroparticle Physics Group, Center for Theoretical Physics of the Universe, Institute for Basic Science, Daejeon 34126, Korea

  • *Contact author: rhb@physics.mcgill.ca
  • †Contact author: juerg@phys.ethz.ch
  • ‡Contact author: hao.jiao@mail.mcgill.ca
PDF

Phys. Rev. Lett. 136, 031001 – Published 21 January, 2026

DOI: https://doi.org/10.1103/ys32-853g

Abstract

We propose a mechanism for the generation of magnetic fields on cosmological scales that is operative after recombination. An essential ingredient is an instability (of parametric resonance type) of the electromagnetic field driven by an oscillating pseudoscalar dark-matter field, ϕ, that is coupled to the electromagnetic field tensor via a ϕF∧F term in the Lagrangian of axion electrodynamics. We find that magnetic fields larger than the observational lower bounds can be generated soon after recombination on scales of 1 Mpc.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (49)

  1. A. Kandus, K. E. Kunze, and C. G. Tsagas, Primordial magnetogenesis, Phys. Rep. 505, 1 (2011).
  2. L. M. Widrow, Origin of galactic and extragalactic magnetic fields, Rev. Mod. Phys. 74, 775 (2002).
  3. R. Durrer and A. Neronov, Cosmological magnetic fields: Their generation, evolution and observation, Astron. Astrophys. Rev. 21, 62 (2013).
  4. T. Vachaspati, Progress on cosmological magnetic fields, Rep. Prog. Phys. 84, 074901 (2021).
  5. A. M. Taylor, I. Vovk, and A. Neronov, Extragalactic magnetic fields constraints from simultaneous GeV-TeV observations of blazars, Astron. Astrophys. 529, A144 (2011).

  6. There is also a robust upper bound on the strength of the magnetic field of B<10−9Gauss on these scales derived from the nonobservation of magnetic field signals in the cosmic microwave background [7]. There are lower bounds [8] that come from the Fermi-LAT, H.E.S.S., and VERITAS studies of cascade emission from blazars that are quite close to the lower bound mentioned above.

  7. J. D. Barrow, P. G. Ferreira, and J. Silk, Constraints on a primordial magnetic field, Phys. Rev. Lett. 78, 3610 (1997).
  8. M. Ackermann et al. (Fermi-LAT Collaboration), The search for spatial extension in high-latitude sources detected by the Fermi Large Area Telescope, Astrophys. J. Suppl. Ser. 237, 32 (2018). S. Archambault et al. (VERITAS Collaboration), Search for magnetically broadened cascade emission from blazars with VERITAS, Astrophys. J. 835, 288 (2017); A. Abramowski et al. (H.E.S.S. Collaboration), Search for extended γ-ray emission around AGN with H.E.S.S. and Fermi-LAT, Astron. Astrophys. 562, A145 (2014).
  9. M. S. Turner and L. M. Widrow, Inflation produced, large scale magnetic fields, Phys. Rev. D 37, 2743 (1988).
  10. B. Ratra, Cosmological “seed” magnetic field from inflation, Astrophys. J. Lett. 391, L1 (1992).
  11. S. M. Carroll, G. B. Field, and R. Jackiw, Limits on a Lorentz and parity violating modification of electrodynamics, Phys. Rev. D 41, 1231 (1990).
  12. W. D. Garretson, G. B. Field, and S. M. Carroll, Primordial magnetic fields from pseudo-Goldstone bosons, Phys. Rev. D 46, 5346 (1992).
  13. G. B. Field and S. M. Carroll, Cosmological magnetic fields from primordial helicity, Phys. Rev. D 62, 103008 (2000).
  14. J. Frohlich and B. Pedrini, New applications of the chiral anomaly, arXiv:hep-th/0002195.
  15. J. Frohlich and B. Pedrini, Axions, quantum mechanical pumping, and primeval magnetic fields, arXiv:cond-mat/0201236.
  16. M. Joyce and M. E. Shaposhnikov, Primordial magnetic fields, right-handed electrons, and the Abelian anomaly, Phys. Rev. Lett. 79, 1193 (1997).
  17. A. Boyarsky, J. Frohlich, and O. Ruchayskiy, Self-consistent evolution of magnetic fields and chiral asymmetry in the early Universe, Phys. Rev. Lett. 108, 031301 (2012).

  18. This mechanism has been explored in the context of inflation in many works (see, e.g., Refs. [19, 20].) A potential parametric resonance instability was discussed in [21, 22], and in [20, 23, 24] it was emphasized that the resulting magnetic field will be helical.

  19. M. M. Anber and L. Sorbo, N-flationary magnetic fields, J. Cosmol. Astropart. Phys. 10 (2006) 018.
  20. R. Durrer, L. Hollenstein, and R. K. Jain, Can slow roll inflation induce relevant helical magnetic fields?, J. Cosmol. Astropart. Phys. 03 (2011) 037.
  21. T. Fujita, R. Namba, Y. Tada, N. Takeda, and H. Tashiro, Consistent generation of magnetic fields in axion inflation models, J. Cosmol. Astropart. Phys. 05 (2015) 054.
  22. P. Adshead, J. T. Giblin, T. R. Scully, and E. I. Sfakianakis, Magnetogenesis from axion inflation, J. Cosmol. Astropart. Phys. 10 (2016) 039.
  23. L. Campanelli, Helical magnetic fields from inflation, Int. J. Mod. Phys. D 18, 1395 (2009); L. Campanelli and M. Giannotti, Magnetic helicity generation from the cosmic axion field, Phys. Rev. D 72, 123001 (2005).
  24. C. Caprini and L. Sorbo, Adding helicity to inflationary magnetogenesis, J. Cosmol. Astropart. Phys. 10 (2014) 056.
  25. T. Vachaspati, Magnetic fields from cosmological phase transitions, Phys. Lett. B 265, 258 (1991).
  26. E. G. M. Ferreira, Ultra-light dark matter, Astron. Astrophys. Rev. 29, 7 (2021).
  27. L. Hui, Wave dark matter, Annu. Rev. Astron. Astrophys. 59, 247 (2021).

  28. An initial misalignment of an axion field from the minimum of the low energy effective potential is often argued to be a consequence of a period of primordial cosmological inflation exponentially expanding an initial fluctuation patch (see, e.g., Ref. [29] for a textbook discussion of this mechanism). However, if the breaking of the global symmetry that leads to the axion field occurs during the standard big bang phase of cosmological evolution, this justification of an initial misalignment will not work. On the other hand, global symmetries must be broken at the Planck scale, and it has recently been shown [30] that these symmetry breaking effects will naturally deposit the axion field initially at a value that is misaligned from the low energy minimum uniformly over all of space (see also Ref. [31]). Since the density fluctuations are small before recombination and since low mass ϕ fields are very weakly interacting (modulo the instability that we describe and that sets in at the time of recombination), the coherence of the ϕ condensate will be maintained from when it starts to oscillate until the time of recombination.

  29. E. W. Kolb and M. S. Turner, The early universe, Front. Phys. 69, 1 (1990).
  30. R. Brandenberger, Non-inflationary axion and ALP misalignment mechanism, Phys. Rev. D 112, 103523 (2025).
  31. L. Di Luzio, B. Gavela, P. Quilez, and A. Ringwald, Dark matter from an even lighter QCD axion: Trapped misalignment, J. Cosmol. Astropart. Phys. 10 (2021) 001; L. Di Luzio and P. Sørensen, Axion production via trapped misalignment from Peccei-Quinn symmetry breaking, J. High Energy Phys. 10 (2024) 239.
  32. E. McDonough, H. Bazrafshan Moghaddam, and R. H. Brandenberger, Preheating and entropy perturbations in axion monodromy inflation, J. Cosmol. Astropart. Phys. 05 (2016) 012.
  33. H. Bazrafshan Moghaddam, E. McDonough, R. Namba, and R. H. Brandenberger, Inflationary magneto-(non)genesis, increasing kinetic couplings, and the strong coupling problem, Classical Quantum Gravity 35, 105015 (2018).
  34. R. Brandenberger, V. Kamali, and R. O. Ramos, Decay of ALP condensates via gravitation-induced resonance, J. Cosmol. Astropart. Phys. 11 (2023) 009.
  35. R. Brandenberger, P. C. M. Delgado, A. Ganz, and C. Lin, Graviton to photon conversion via parametric resonance, Phys. Dark Universe 40, 101202 (2023).
  36. J. H. Traschen and R. H. Brandenberger, Particle production during out-of-equilibrium phase transitions, Phys. Rev. D 42, 2491 (1990).
  37. A. D. Dolgov and D. P. Kirilova, On particle creation by a time dependent scalar field, Sov. J. Nucl. Phys. 51, 172 (1990) Yad. Fiz. 51, 273 (1990).
  38. V. Iršič, M. Viel, M. G. Haehnelt, J. S. Bolton, and G. D. Becker, First constraints on fuzzy dark matter from Lyman-α forest data and hydrodynamical simulations, Phys. Rev. Lett. 119, 031302 (2017).
  39. D. Y. Cheong, N. L. Rodd, and L. T. Wang, A quantum description of wave dark matter, Phys. Rev. D 111, 015028 (2025).
  40. SvP. Svrcek and E. Witten, Axions in string theory, J. High Energy Phys. 06 (2006) 051.
  41. H. Bernardo, R. Brandenberger, and J. Fröhlich, Towards a dark sector model from string theory, J. Cosmol. Astropart. Phys. 09 (2022) 040.
  42. D. J. E. Marsh, Axion cosmology, Phys. Rep. 643, 1 (2016).
  43. Ciaran O’Hare’s website, http://cajihare.github.io/AxionLimits/.

  44. After the time of recombination, there are still free electrons present. Since we know that the CMB photons travel without scattering from recombination to today, we can derive an upper bound on the effective conductance of matter (the conductance induced by the residual charged particles that remain after recombination) σeff≪10−29  eV. Given this bound on σeff it can easily be checked that for values of k corresponding to the scale of cosmological magnetic fields the effects of σeff on the evolution of the magnetic field in our setup is negligible.

  45. R. Allahverdi, R. Brandenberger, F. Y. Cyr-Racine, and A. Mazumdar, Reheating in inflationary cosmology: Theory and applications, Annu. Rev. Nucl. Part. Sci. 60, 27 (2010).
  46. H. Jiao, R. Brandenberger, and V. Kamali, Direct collapse supermassive black holes from ultralight dark matter, Phys. Rev. D 112, 043546 (2025).
  47. D. S. Lee, W. L. Lee, and K. W. Ng, Primordial magnetic fields from dark energy, Phys. Lett. B 542, 1 (2002).
  48. N. Banik and A. J. Christopherson, Recombination era magnetic fields from axion dark matter, Phys. Rev. D 93, 043003 (2016).
  49. K. Choi, H. Kim, and T. Sekiguchi, Late-time magnetogenesis driven by axionlike particle dark matter and a dark photon, Phys. Rev. Lett. 121, 031102 (2018).

Outline

Information

Phys. Rev. Lett. 136, 031001– Published 21 January, 2026
  • Received 23 May 2025
  • Revised 4 August 2025
  • Accepted 15 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