Cosmic voids are the least contaminated environments in the large-scale structure, so their interior magnetic fields — too weak for dynamos or structure-formation shocks to have modified — are the only plausible present-day relics of the primordial magnetic seed. Rodríguez-Medrano, Stasyszyn, Paz & Springel (2023) showed in the IllustrisTNG simulation that void interiors preserve a uniform primordial seed essentially unchanged, but flagged that the seed used is a physically unmotivated uniform field along one axis, and left open whether void fields could ever be detected and confirmed as primordial. The open problem is whether a cosmologically realistic, tangled primordial seed leaves statistically distinguishable signatures in void interiors; whether individual void fields are detectable with current or near-future Faraday-rotation or gamma-ray observations; and whether any detection could be attributed to a primordial rather than astrophysical origin.

Background

Galaxies and the hot plasma of galaxy clusters carry magnetic fields of order microgauss, but the origin of these fields is unknown. Two families of explanations compete: astrophysical scenarios, in which fields are generated inside stars and active galaxies and then carried into intergalactic space by winds and outflows, and primordial scenarios, in which a weak field was generated in the early universe (for example during inflation or a cosmological phase transition — physics beyond the Standard Model) and was later amplified by structure formation and turbulent dynamos, i.e. by the random stretching, twisting and folding of field lines by turbulent plasma motion. Because nonlinear amplification erases the memory of the initial conditions inside galaxies and clusters, the least dense regions of the universe — cosmic voids, the near-empty volumes tens of megaparsecs across that occupy most of space in the cosmic web of filaments, sheets and clusters — are the only places where a primordial field might survive essentially unchanged, diluted only by cosmic expansion.

Two observational probes are central. First, Faraday rotation: when polarized radio emission passes through a magnetized plasma, its polarization angle rotates by an angle proportional to the wavelength squared, with proportionality constant the rotation measure (RM), the line-of-sight integral of the free-electron density times the line-of-sight magnetic-field component. Grids of RM measurements of large samples of background radio sources (e.g. from the LOFAR (Low-Frequency Array) Two-Metre Sky Survey, LoTSS) can statistically probe magnetized gas in the foreground cosmic web; because void gas is extremely tenuous, its RM contribution is correspondingly minute. Second, gamma-ray cascades: very-high-energy (TeV) photons from blazars (active galactic nuclei with relativistic jets pointed at us) pair-produce on background radiation, and the resulting electron–positron pairs inverse-Compton scatter background light into GeV photons; a weak intergalactic magnetic field deflects the pairs, broadening or suppressing this GeV 'pair halo'. The non-observation of such halos gives lower bounds on intergalactic (void) fields of order 10−1610^{-16}–10−1510^{-15} G (Neronov & Vovk 2010), though the interpretation is debated — beam–plasma instabilities have been proposed as an alternative way to drain the pair beams without magnetic deflection (Broderick, Chang & Pfrommer 2012).

On the theoretical side, cosmological magneto-hydrodynamic (MHD) simulations follow magnetic fields through structure formation. The IllustrisTNG suite (Marinacci et al. 2018) seeds its runs with a primordial field of 10−1410^{-14} comoving Gauss that is perfectly uniform and points along a single Cartesian axis (zz); this choice is explicitly one of numerical convenience — a homogeneous field automatically satisfies the divergence-free condition ∇⋅B=0\nabla\cdot\mathbf{B}=0 that MHD requires — rather than physics. A realistic primordial field from inflation or a phase transition would instead be stochastic ('tangled'), characterized by a power spectrum and a finite coherence length, with no preferred direction. Separately, simulations with the ENZO cosmological magneto-hydrodynamics code (Vazza et al. 2017, 2020) have evolved different stochastic primordial-field models and find that voids retain traces of the seed's amplitude and topology, with void magnetization differing by more than an order of magnitude between seed models — but without IllustrisTNG's full galaxy-formation ('subgrid') physics.

Rodríguez-Medrano et al. (2023) analyzed the TNG100 run (the intermediate-volume run of the IllustrisTNG suite): identifying cosmic voids with the Popcorn void-finding code, which selects spherical regions in the galaxy distribution whose integrated density contrast is below a fixed limit, they found that within roughly 0.80.8 void radii the field keeps its initial, seed-aligned direction — the median squared component along the seed axis stays elevated, converging to the isotropic value 1/31/3 only near the void boundary — implying that void interiors evolve the seed by cosmic expansion alone. They also found that, at fixed stellar mass, galaxies inside voids carry slightly weaker halo-averaged fields (BhaloB_{\rm halo}, the volume-weighted mean field strength within the halo) than galaxies elsewhere, while the inner galactic fields (BdiskB_{\rm disk}) show no environmental difference. Their conclusions flag the artificial seed direction and suggest that detected void fields, if any, could carry primordial information. Whether a detected void field could be attributed to a primordial rather than astrophysical origin is itself actively contested in the recent literature (e.g., Garg, Durrer & Schober 2025; Seller & Sigl 2026).

Problem Statement

Determine whether the magnetic fields in the interiors of cosmic voids can be established as identifiable relics of the primordial magnetic seed field. Concretely, three linked questions, in the generality left open by Rodríguez-Medrano et al. (2023):

  1. (Prediction) In cosmological magneto-hydrodynamic simulations with realistic galaxy-formation physics, does a cosmologically realistic — stochastic, tangled — primordial seed field, specified by its power spectrum and coherence length, leave signatures in void interiors that are distinguishable, in observable statistics such as field-strength distributions, coherence lengths, spectral shapes, or anisotropy measures across the void population, from the signatures produced by astrophysical magnetization (magnetized galactic outflows, leakage of galactic dipole fields, turbulent transport)? The uniform single-axis seed of the source study is a numerical convenience, and its void-interior memory result must be re-derived for realistic seeds.

  2. (Detection) Can the magnetic field of individual cosmic voids be detected, and its strength and coherence properties measured, with current or near-future facilities — through Faraday-rotation-measure grids (e.g., LOFAR/LoTSS, the Square Kilometre Array and its precursors, rotation measures of fast radio bursts, i.e. millisecond-duration extragalactic radio flashes) or gamma-ray cascade (pair-halo) observations?

  3. (Attribution) If a void field is detected, can its primordial character be confirmed — i.e., can a primordial origin be distinguished from the astrophysical alternatives (galactic dipole leakage and its plasma screening, outflow pollution, plasma-instability reinterpretation of the cascade data), for example through the spectral shape or coherence scale of the detected field?

All three parts are required; a resolution must reach a definite determination on each, and part 3 must be answered even if part 2 yields a non-detection.

Auxiliary questions left untouched: the physical origin of the small but systematic environmental difference in halo magnetic fields (BhaloB_{\rm halo}) between void and non-void galaxies at fixed stellar mass, and the robustness of all void-field results to simulation volume, resolution, subgrid-physics model, and cosmic variance across larger void samples.

References

  1. Agustín M. Rodríguez-Medrano, Federico A. Stasyszyn, Dante J. Paz, Volker Springel (2023), 'Magnetic Fields in Cosmic Voids', arXiv:2305.01765, DOI 10.48550/arXiv.2305.01765, https://arxiv.org/abs/2305.01765
  2. Federico Marinacci, Mark Vogelsberger, Rüdiger Pakmor, Paul Torrey, Volker Springel, Lars Hernquist, Dylan Nelson, Rainer Weinberger, Annalisa Pillepich, Jill Naiman, Shy Genel (2018), 'First results from the IllustrisTNG simulations: radio haloes and magnetic fields', MNRAS 480, 5113, arXiv:1707.03396, DOI 10.1093/mnras/sty2206, https://arxiv.org/abs/1707.03396
  3. Andrii Neronov, Ievgen Vovk (2010), 'Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars', Science 328, 73, arXiv:1006.3504, DOI 10.1126/science.1184192, https://arxiv.org/abs/1006.3504
  4. Avery E. Broderick, Philip Chang, Christoph Pfrommer (2012), 'The Cosmological Impact of Luminous TeV Blazars I: Implications of Plasma Instabilities for the Intergalactic Magnetic Field and Extragalactic Gamma-Ray Background', ApJ 752, 22, arXiv:1106.5494, DOI 10.1088/0004-637X/752/1/22, https://arxiv.org/abs/1106.5494
  5. Takuya Akahori, Dongsu Ryu, B. M. Gaensler (2016), 'Fast Radio Bursts as Probes of Magnetic Fields in the Intergalactic Medium', ApJ 824, 105, arXiv:1602.03235, DOI 10.3847/0004-637X/824/2/105, https://arxiv.org/abs/1602.03235
  6. F. Vazza, M. Brüggen, C. Gheller, S. Hackstein, D. Wittor, P. M. Hinz (2017), 'Simulations of extragalactic magnetic fields and of their observables', Classical and Quantum Gravity 34, 234001, arXiv:1711.02669, DOI 10.1088/1361-6382/aa8e60, https://arxiv.org/abs/1711.02669
  7. F. Vazza, D. Paoletti, S. Banfi, F. Finelli, C. Gheller, S. O'Sullivan, M. Brüggen (2020), 'Simulations and observational tests of primordial magnetic fields from Cosmic Microwave Background constraints', MNRAS 500, 5350, arXiv:2009.01539, DOI 10.1093/mnras/staa3532, https://arxiv.org/abs/2009.01539
  8. Andres Aramburo-Garcia, Kyrylo Bondarenko, Alexey Boyarsky, Andrii Neronov, Anna Scaife, Anastasia Sokolenko (2022), 'Revision of Faraday rotation measure constraints on the primordial magnetic field using the IllustrisTNG simulation', MNRAS 515, 5673, arXiv:2204.05918, DOI 10.1093/mnras/stac2058, https://arxiv.org/abs/2204.05918
  9. J. Blunier, A. Neronov (2024), 'Constraint on magnetized galactic outflows from LOFAR rotation measure data', A&A 691, A34, arXiv:2403.13418, DOI 10.1051/0004-6361/202450138, https://arxiv.org/abs/2403.13418
  10. Kyrylo Bondarenko, Alexey Boyarsky, Anastasia Sokolenko, Ievgen Vovk (2024), 'Probing intergalactic intergalactic magnetic fields with LOFAR LoTSS DR2 data', arXiv:2404.17402, DOI 10.48550/arXiv.2404.17402, https://arxiv.org/abs/2404.17402
  11. A. Neronov, F. Vazza, S. Mtchedlidze, E. Carretti (2024), 'Revision of upper bound on volume-filling intergalactic magnetic fields with LOFAR', arXiv:2412.14825, DOI 10.48550/arXiv.2412.14825, https://arxiv.org/abs/2412.14825
  12. Deepen Garg, Ruth Durrer, Jennifer Schober (2025), 'Are magnetic fields in cosmic voids primordial?', arXiv:2505.14774, DOI 10.48550/arXiv.2505.14774, https://arxiv.org/abs/2505.14774
  13. Károly Seller, Günter Sigl (2026), 'The contribution of galaxies to the magnetic field in cosmic voids', A&A 709, A45, DOI 10.1051/0004-6361/202558395, arXiv:2510.08025, https://arxiv.org/abs/2510.08025
  14. Matías Sotomayor Webar, Yosef Abed, Dieter Horns (2025), 'Discovery of femto Gauss intergalactic magnetic fields towards Mkn 501', arXiv:2509.11996, DOI 10.48550/arXiv.2509.11996, https://arxiv.org/abs/2509.11996
  15. Yuri Yamashita, Hiroyuki Tashiro, Kiyotomo Ichiki (2026), 'Turbulent Transport of Galactic Magnetic Fields into Cosmic Voids: Insights from IllustrisTNG', arXiv:2607.09484, DOI 10.48550/arXiv.2607.09484, https://arxiv.org/abs/2607.09484