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Primordial magnetic field from chiral plasma instability with sourcing

Murman Gurgenidze1,2,*, Andrew J. Long3,†, Alberto Roper Pol4,‡, Axel Brandenburg1,2,5,6,§, and Tina Kahniashvili1,2,7,∥

  • *Contact author: mgurgeni@andrew.cmu.edu
  • †Contact author: andrewjlong@rice.edu
  • ‡Contact author: alberto.roperpol@unige.ch
  • §Contact author: brandenb@nordita.org
  • ∥Contact author: tinatin@andrew.cmu.edu
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Phys. Rev. D 114, 023542 – Published 21 July, 2026

DOI: https://doi.org/10.1103/7lpb-9yvw

Abstract

In an electron-positron plasma, an imbalance in the number of right- and left-chiral particles can lead to the growth of a helical magnetic field through a phenomenon called the chiral plasma instability (CPI). In the early Universe, scattering reactions that violate chirality come into thermal equilibrium when the plasma cools below a temperature of approximately 80 TeV. Since these reactions tend to relax any preexisting chiral asymmetry to zero as the system approaches equilibrium, the standard lore is that primordial magnetogenesis via the CPI is not viable below 80 TeV. In this work, we propose that the presence of a source for chirality can allow the CPI to operate even below 80 TeV, we explore the implications of this scenario, and we derive predictions for the resultant magnetic field helicity using a combination of analytical methods and direct numerical simulation.

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References (72)

  1. A. D. Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, Pis’ma Zh. Eksp. Teor. Fiz. 5, 32 (1967).
  2. A. Pilaftsis, CP violation and baryogenesis due to heavy Majorana neutrinos, Phys. Rev. D 56, 5431 (1997).
  3. M. E. Shaposhnikov, Baryon asymmetry of the universe in standard electroweak theory, Nucl. Phys. B287, 757 (1987).
  4. A. Vilenkin, Equilibrium parity violating current in a magnetic field, Phys. Rev. D 22, 3080 (1980).
  5. M. Joyce and M. E. Shaposhnikov, Primordial magnetic fields, right-handed electrons, and the Abelian anomaly, Phys. Rev. Lett. 79, 1193 (1997).
  6. A. Boyarsky, J. Fröhlich, and O. Ruchayskiy, Self-consistent evolution of magnetic fields and chiral asymmetry in the early Universe, Phys. Rev. Lett. 108, 031301 (2012).
  7. A. Boyarsky, O. Ruchayskiy, and M. Shaposhnikov, Long-range magnetic fields in the ground state of the standard model plasma, Phys. Rev. Lett. 109, 111602 (2012).
  8. H. Tashiro, T. Vachaspati, and A. Vilenkin, Chiral effects and cosmic magnetic fields, Phys. Rev. D 86, 105033 (2012).
  9. Y. Akamatsu and N. Yamamoto, Chiral plasma instabilities, Phys. Rev. Lett. 111, 052002 (2013).
  10. A. Ohnishi and N. Yamamoto, Magnetars and the chiral plasma instabilities, arXiv:1402.4760.
  11. D. Grabowska, D. B. Kaplan, and S. Reddy, Role of the electron mass in damping chiral plasma instability in Supernovae and neutron stars, Phys. Rev. D 91, 085035 (2015).
  12. A. Boyarsky, J. Fröhlich, and O. Ruchayskiy, Magnetohydrodynamics of chiral relativistic fluids, Phys. Rev. D 92, 043004 (2015).
  13. G. Sigl and N. Leite, Chiral magnetic effect in protoneutron stars and magnetic field spectral evolution, J. Cosmol. Astropart. Phys. 01 (2016) 025.
  14. A. J. Long and E. Sabancilar, Chiral charge erasure via thermal fluctuations of magnetic helicity, J. Cosmol. Astropart. Phys. 05 (2016) 029.
  15. P. Pavlović, N. Leite, and G. Sigl, Chiral magnetohydrodynamic turbulence, Phys. Rev. D 96, 023504 (2017).
  16. I. Rogachevskii, O. Ruchayskiy, A. Boyarsky, J. Fröhlich, N. Kleeorin, A. Brandenburg, and J. Schober, Laminar and turbulent dynamos in chiral magnetohydrodynamics-I: Theory, Astrophys. J. 846, 153 (2017).
  17. A. Brandenburg, J. Schober, I. Rogachevskii, T. Kahniashvili, A. Boyarsky, J. Fröhlich, O. Ruchayskiy, and N. Kleeorin, The turbulent chiral-magnetic cascade in the early universe, Astrophys. J. Lett. 845, L21 (2017).
  18. J. Schober, I. Rogachevskii, A. Brandenburg, A. Boyarsky, J. Fröhlich, O. Ruchayskiy, and N. Kleeorin, Laminar and turbulent dynamos in chiral magnetohydrodynamics. II. Simulations, Astrophys. J. 858, 124 (2018).
  19. P. Pavlović and G. Sigl, On minimal energy states of chiral MHD turbulence, J. Cosmol. Astropart. Phys. 04 (2019) 055.
  20. J. Schober, I. Rogachevskii, and A. Brandenburg, Dynamo instabilities in plasmas with inhomogeneous chiral chemical potential, Phys. Rev. D 105, 043507 (2022).
  21. J. Schober, I. Rogachevskii, and A. Brandenburg, Chiral anomaly and dynamos from inhomogeneous chemical potential fluctuations, Phys. Rev. Lett. 132, 065101 (2024).
  22. M. Giovannini, Anomalous magnetohydrodynamics, Phys. Rev. D 88, 063536 (2013).
  23. N. Yamamoto, Scaling laws in chiral hydrodynamic turbulence, Phys. Rev. D 93, 125016 (2016).
  24. K. Hattori, Y. Hirono, H.-U. Yee, and Y. Yin, MagnetoHydrodynamics with chiral anomaly: Phases of collective excitations and instabilities, Phys. Rev. D 100, 065023 (2019).
  25. K. Fukushima, D. E. Kharzeev, and H. J. Warringa, The chiral magnetic effect, Phys. Rev. D 78, 074033 (2008).
  26. D. E. Kharzeev, The chiral magnetic effect and anomaly-induced transport, Prog. Part. Nucl. Phys. 75, 133 (2014).
  27. J. Liao, Anomalous transport effects and possible environmental symmetry ‘violation’ in heavy-ion collisions, Pramana 84, 901 (2015).
  28. D. E. Kharzeev, J. Liao, S. A. Voloshin, and G. Wang, Chiral magnetic and vortical effects in high-energy nuclear collisions—A status report, Prog. Part. Nucl. Phys. 88, 1 (2016).
  29. K. Kamada, N. Yamamoto, and D.-L. Yang, Chiral effects in astrophysics and cosmology, Prog. Part. Nucl. Phys. 129, 104016 (2023).
  30. D. E. Kharzeev, Chiral magnetic effect: A brief introduction, in Handbook of Nuclear Physics, edited by I. Tanihata, H. Toki, and T. Kajino (Springer Nature, Singapore, 2023), pp. 1–14.
  31. W. Li, Q. Shou, and F. Wang, Experimental review on the chiral magnetic effect in relativistic heavy ion collisions, Eur. Phys. J. Spec. Top. (2026).
  32. A. Neronov and I. Vovk, Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars, Science 328, 73 (2010).
  33. R. Durrer and A. Neronov, Cosmological magnetic fields: Their generation, evolution and observation, Astron. Astrophys. Rev. 21, 62 (2013).
  34. K. Jedamzik and A. Saveliev, Stringent limit on primordial magnetic fields from the cosmic microwave background radiation, Phys. Rev. Lett. 123, 021301 (2019).
  35. K. Subramanian, From primordial seed magnetic fields to the galactic dynamo, Galaxies 7, 47 (2019).
  36. T. Vachaspati, Progress on cosmological magnetic fields, Rep. Prog. Phys. 84, 074901 (2021).
  37. K. Jedamzik and T. Abel, Weak primordial magnetic fields and anisotropies in the cosmic microwave background radiation, arXiv:1108.2517.
  38. K. Jedamzik and L. Pogosian, Relieving the Hubble tension with primordial magnetic fields, Phys. Rev. Lett. 125, 181302 (2020).
  39. S. Galli, L. Pogosian, K. Jedamzik, and L. Balkenhol, Consistency of Planck, ACT, and SPT constraints on magnetically assisted recombination and forecasts for future experiments, Phys. Rev. D 105, 023513 (2022).
  40. S. H. Mirpoorian, K. Jedamzik, and L. Pogosian, Modified recombination and the Hubble tension, Phys. Rev. D 111, 083519 (2025).
  41. K. Jedamzik, L. Pogosian, and T. Abel, Hints of primordial magnetic fields at recombination and implications for the Hubble tension, Nat. Astron. 10, 317 (2026).
  42. B. A. Campbell, S. Davidson, J. R. Ellis, and K. A. Olive, Cosmological baryon asymmetry constraints on extensions of the standard model, Phys. Lett. B 256, 484 (1991).
  43. D. Bödeker and D. Schröder, Equilibration of right-handed electrons, J. Cosmol. Astropart. Phys. 05 (2019) 010.
  44. J. Schober, A. Brandenburg, and I. Rogachevskii, Chiral fermion asymmetry in high-energy plasma simulations, Geophys. Astrophys. Fluid Dyn. 114, 106 (2020).
  45. J. Schober, J. Schober, T. Fujita, T. Fujita, R. Durrer, and R. Durrer, Generation of chiral asymmetry via helical magnetic fields, Phys. Rev. D 101, 103028 (2020).
  46. A. Brandenburg, Y. He, T. Kahniashvili, M. Rheinhardt, and J. Schober, Relic gravitational waves from the chiral magnetic effect, Astrophys. J. 911, 110 (2021).
  47. J. Schober, I. Rogachevskii, and A. Brandenburg, Production of a chiral magnetic anomaly with emerging turbulence and mean-field dynamo action, Phys. Rev. Lett. 128, 065002 (2022).
  48. J. Schober, I. Rogachevskii, and A. Brandenburg, Efficiency of dynamos from an autonomous generation of chiral asymmetry, Phys. Rev. D 110, 043515 (2024).
  49. E. K. Akhmedov, V. A. Rubakov, and A. Y. Smirnov, Baryogenesis via neutrino oscillations, Phys. Rev. Lett. 81, 1359 (1998).
  50. M. Trodden, Electroweak baryogenesis, Rev. Mod. Phys. 71, 1463 (1999).
  51. J. M. Cline, Baryogenesis, in Les Houches Summer School—Session 86: Particle Physics and Cosmology: The Fabric of Spacetime (Elsevier, Amsterdam, 2006), .
  52. G. Elor, M. Escudero, and A. Nelson, Baryogenesis and dark matter from B mesons, Phys. Rev. D 99, 035031 (2019).
  53. A. E. Nelson and H. Xiao, Baryogenesis from B meson oscillations, Phys. Rev. D 100, 075002 (2019).
  54. J. Klarić, M. Shaposhnikov, and I. Timiryasov, Reconciling resonant leptogenesis and baryogenesis via neutrino oscillations, Phys. Rev. D 104, 055010 (2021).
  55. A. Brandenburg, K. Enqvist, and P. Olesen, Large scale magnetic fields from hydromagnetic turbulence in the very early universe, Phys. Rev. D 54, 1291 (1996).
  56. A. Roper Pol and A. S. Midiri, Relativistic magnetohydrodynamics in the early Universe, arXiv:2501.05732.
  57. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Westview Press, Boulder, Colorado, 1995).
  58. A. Brandenburg, K. Kamada, K. Mukaida, K. Schmitz, and J. Schober, Chiral magnetohydrodynamics with zero total chirality, Phys. Rev. D 108, 063529 (2023).
  59. MAGIC Collaboration, A lower bound on intergalactic magnetic fields from time variability of 1ES 0229+200 from MAGIC and Fermi/LAT observations, Astron. Astrophys. 670, A145 (2023).
  60. T. Fujita and K. Kamada, Large-scale magnetic fields can explain the baryon asymmetry of the Universe, Phys. Rev. D 93, 083520 (2016).
  61. K. Kamada and A. J. Long, Baryogenesis from decaying magnetic helicity, Phys. Rev. D 94, 063501 (2016).
  62. K. Kamada and A. J. Long, Evolution of the baryon asymmetry through the electroweak crossover in the presence of a helical magnetic field, Phys. Rev. D 94, 123509 (2016).
  63. Y. Hamada, K. Mukaida, and F. Uchida, Symmetries of hot SM, magnetic flux baryogenesis from helicity decay, J. High Energy Phys. 01 (2026) 040.
  64. H. Fukuda, Y. Hamada, K. Kamada, K. Mukaida, and F. Uchida, Magnetic helicity, magnetic monopoles, and Higgs winding, J. High Energy Phys. 03 (2026) 127.
  65. W. Chao, Chiral magnetic effect induced spectator process for leptogenesis, arXiv:2511.13051.
  66. A. Brandenburg, E. Clarke, T. Kahniashvili, A. J. Long, and G. Sun, Relic gravitational waves from the chiral plasma instability in the standard cosmological model, Phys. Rev. D 109, 043534 (2024).
  67. P. B. Arnold, G. D. Moore, and L. G. Yaffe, Transport coefficients in high temperature gauge theories (I). Leading log results, J. High Energy Phys. 11 (2000) 001.
  68. pencil code collaboration, The pencil code, a modular MPI code for partial differential equations and particles: Multipurpose and multiuser-maintained, J. Open Source Software 6, 2807 (2021).
  69. A. Brandenburg, T. Kahniashvili, S. Mandal, A. Roper Pol, A. G. Tevzadze, and T. Vachaspati, Evolution of hydromagnetic turbulence from the electroweak phase transition, Phys. Rev. D 96, 123528 (2017).
  70. The pencil code, 10.5281/zenodo.2315093.
  71. Datasets for Primordial magnetic field from chiral plasma instability with sourcing v.2025.08.12, 10.5281/zenodo.17852669.
  72. Public code for reproducing results of this work, https://github.com/cosmoGW/cosmoGW.

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Phys. Rev. D 114, 023542– Published 21 July, 2026
  • Received 19 December 2025
  • Accepted 8 June 2026
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