arxiv: 2605.05323 · v1 · submitted 2026-05-06 · 🌌 astro-ph.CO

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Primordial Magnetic Fields at Cosmic Dawn: 21-cm Forecasts with HERA and SKA

Keduse Worku , Hector Afonso G. Cruz , Marc Kamionkowski

Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:14 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords primordial magnetic fields21-cm signalcosmic dawnHERASKAsmall-scale structurereionizationearly galaxy formation

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The pith

Primordial magnetic fields can accelerate the formation of the first galaxies and leave measurable shifts in the 21-centimeter signal from cosmic dawn.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that primordial magnetic fields add extra small-scale fluctuations to the matter distribution, which increases the number of low-mass dark matter halos at cosmic dawn. This boost speeds up the processes of Lyman-alpha coupling, X-ray heating, and the start of reionization, creating correlated changes in both the average and fluctuating 21-centimeter radio signals from the early universe. By adding a physically motivated magnetic term to an existing fast analytic model of these signals, the work produces forecasts for how strongly HERA and SKA observations could detect or limit such fields when combined with cosmic microwave background data. A sympathetic reader would care because this opens a new route to learning about magnetic fields from the first instants after the big bang using telescopes that will soon be online.

Core claim

Primordial magnetic fields source additional small-scale matter fluctuations that raise the abundance of low-mass halos during cosmic dawn. This enhancement accelerates Lyman-alpha coupling, X-ray heating, and reionization, producing correlated shifts in the global and fluctuating 21-centimeter signals. Extending the zeus21 framework to incorporate a PMF contribution to the linear matter power spectrum, with radiative damping before recombination and suppression below the magnetic Jeans scale, preserves computational speed while enabling forecasts across a range of field amplitudes for spectral index n_B = -2.9. When 21-centimeter forecasts from HERA and SKA are combined with external CMBpri

What carries the argument

The extension of the zeus21 analytic framework to add a physically motivated PMF term to the linear matter power spectrum, including radiative damping before recombination and magnetic-pressure suppression below the magnetic Jeans scale; this term directly increases the predicted abundance of low-mass halos and thereby shifts the timing of 21-centimeter features.

If this is right

For a spectral index of -2.9, stronger primordial magnetic fields produce progressively earlier Lyman-alpha coupling, X-ray heating, and reionization, shifting the peak and shape of the 21-centimeter global signal and increasing power on relevant scales.
The modified model generates concrete forecasts showing that HERA and SKA data can detect or place upper limits on magnetic field amplitudes through their effect on early structure.
Combining the 21-centimeter forecasts with CMB priors yields constraints on primordial magnetic fields that are independent of those obtained from other cosmological probes.
The extended framework keeps the original speed and modularity, allowing rapid scans over magnetic field parameters without new full simulations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the modeled effect holds, similar 21-centimeter shifts could help distinguish primordial magnetic fields from other early-universe modifications to small-scale power, such as warm dark matter.
A positive detection would tighten limits on magnetogenesis scenarios operating before recombination and would motivate targeted searches in high-redshift galaxy surveys.
The same modeling approach could be applied to other mechanisms that alter the small-scale matter spectrum to produce joint forecasts for multiple early-universe physics effects.
Future refinements might incorporate the back-reaction of the enhanced halos on the magnetic field evolution itself.

Load-bearing premise

That adding a term for primordial magnetic fields to the linear matter power spectrum, with the included damping and suppression effects, correctly predicts the resulting increase in low-mass halos and the associated changes in 21-centimeter observables.

What would settle it

A measurement by HERA or SKA showing no earlier shift in the timing of Lyman-alpha coupling or X-ray heating in the 21-centimeter global signal or power spectrum, after the magnetic field strength has been limited by CMB data, would indicate that the modeled enhancement of small-scale structure does not occur.

Figures

Figures reproduced from arXiv: 2605.05323 by Hector Afonso G. Cruz, Keduse Worku, Marc Kamionkowski.

**Figure 1.** Figure 1: FIG. 1. Matter power spectrum (left) and Sheth–Tormen halo mass function ratio relative to ΛCDM, view at source ↗

**Figure 2.** Figure 2: FIG. 2. Global and fluctuating 21-cm observables for varying PMF amplitude view at source ↗

**Figure 3.** Figure 3: FIG. 3. Marginalized Fisher constraints for HERA at fiducial view at source ↗

**Figure 4.** Figure 4: FIG. 4. Same setup as Fig view at source ↗

**Figure 5.** Figure 5: FIG. 5. One-dimensional marginalized constraints on the PMF amplitude view at source ↗

**Figure 6.** Figure 6: FIG. 6. Random-forest prediction of the PMF amplitude view at source ↗

**Figure 7.** Figure 7: FIG. 7. Noise amplitude comparison at fixed redshift view at source ↗

**Figure 8.** Figure 8: FIG. 8. Redshift-resolved Fisher weighting for the PMF-amplitude direction in the baseline setup. view at source ↗

read the original abstract

Primordial magnetic fields (PMFs) can enhance the abundance of low-mass halos during Cosmic Dawn by sourcing additional small-scale matter fluctuations. This enhanced small-scale power can accelerate early galaxy formation, shifting the timing of Lyman-$\alpha$ coupling, X-ray heating, and reionization toward earlier times and imprinting correlated signatures on the global and fluctuating 21-cm signals. We extend the fast analytic framework {\tt\string zeus21} to include a physically motivated PMF contribution to the linear matter power spectrum, including radiative damping before recombination and magnetic-pressure suppression below the magnetic Jeans scale. The implementation preserves the speed and modularity of {\tt\string zeus21}, enabling efficient exploration of PMF parameter space. For $n_B=-2.9$, we quantify the impact of PMFs on early structure formation and 21-cm observables across a range of fiducial magnetic amplitudes, and forecast detectability with \textit{HERA} and \textit{SKA}. Combining 21-cm forecasts with external CMB priors, we find that upcoming experiments can probe PMFs through their impact on small-scale structure, providing constraints complementary to existing cosmological probes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper adds a PMF term to the linear power spectrum inside zeus21 and runs concrete HERA/SKA forecasts, but the mapping from that modified spectrum to halo abundances and 21-cm signals rests on untested approximations.

read the letter

The main takeaway is that the authors take the existing fast zeus21 framework, insert a physically motivated primordial magnetic field contribution to the linear matter power spectrum (with radiative damping and magnetic Jeans suppression), and then produce quantitative forecasts for how this changes early structure formation and the 21-cm signal at cosmic dawn. They keep the code modular and quick, which lets them scan magnetic amplitudes for a spectral index of -2.9 and combine the results with CMB priors to argue for complementary constraints. That part is useful and straightforward to implement. The forecasts themselves are specific enough to be checked against future data. The soft spot sits in the central modeling step. zeus21 uses excursion-set and mean-field approximations for halo mass functions and radiative processes that were not originally tuned for extra small-scale power from PMFs. At the relevant halo masses and redshifts, non-linear collapse, baryonic cooling, and feedback can change how initial power translates into star-formation rate density. The paper does not show direct validation against simulations for this extension, so the size of the predicted shifts in Lyman-alpha coupling, X-ray heating, and reionization timing could be overstated or understated. The stress-test concern about missing non-linear or baryonic effects therefore still applies based on what is described. This is the sort of paper that belongs in a 21-cm or early-universe reading group for the concrete numbers and the complementarity discussion. It deserves a serious referee because the implementation is clear, the forecasts are falsifiable, and the topic is timely, even if reviewers will press on the accuracy of the semi-analytic mapping.

Referee Report

2 major / 2 minor

Summary. The paper extends the analytic semi-numerical code zeus21 to incorporate a PMF contribution to the linear matter power spectrum (including radiative damping before recombination and magnetic-pressure suppression below the magnetic Jeans scale). It then quantifies the resulting enhancement of low-mass halos at Cosmic Dawn for n_B = -2.9, the consequent shifts in Lyman-alpha coupling, X-ray heating and reionization timing, and the imprint on global and fluctuating 21-cm signals. Forecasts for detectability with HERA and SKA are presented, together with the claim that combining these with CMB priors yields complementary constraints on PMF amplitudes.

Significance. If the modeling assumptions hold, the work provides a practical, computationally efficient route to forecasting PMF constraints from upcoming 21-cm arrays via their effect on small-scale structure. The preservation of zeus21's speed and modularity is a clear strength for parameter-space exploration. The significance is limited, however, by the absence of any direct validation of the extended model against simulations that include non-linear gravitational collapse and baryonic physics at the relevant halo masses and redshifts.

major comments (2)

[§3] §3 (Implementation of PMF term in zeus21): the central forecasts rest on the assumption that simply augmenting the linear P(k) with the PMF contribution (radiative damping plus magnetic Jeans suppression) and feeding it into the existing excursion-set halo mass function and mean-field radiative-transfer modules produces reliable shifts in star-formation rate density, Lyman-alpha coupling, and 21-cm observables. No quantitative test of this mapping is shown for M_halo ~ 10^6-10^8 M_sun at z ~ 15-25, where non-linear and baryonic effects are expected to be important.
[§4] §4 (Forecasts and detectability): the claimed complementarity with CMB priors and the projected HERA/SKA constraints are derived directly from the unvalidated zeus21+PMF signals. Without an assessment of systematic uncertainty arising from the linear-P(k) approximation, the forecasted error bars and detection thresholds cannot be taken at face value.

minor comments (2)

[Abstract] The abstract and introduction cite the fiducial spectral index n_B = -2.9 but do not explicitly state the range of magnetic amplitudes explored or the precise definition of the magnetic Jeans scale used in the implementation.
[Figures] Figure captions and axis labels should clarify whether the plotted 21-cm power spectra include the full PMF-modified reionization history or only the linear power-spectrum rescaling.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their constructive comments on the modeling assumptions and forecast robustness. We agree that the semi-analytic nature of the zeus21+PMF extension introduces limitations that warrant clearer discussion, and we have revised the manuscript accordingly to address these points while preserving the work's focus on efficient parameter-space exploration.

read point-by-point responses

Referee: [§3] §3 (Implementation of PMF term in zeus21): the central forecasts rest on the assumption that simply augmenting the linear P(k) with the PMF contribution (radiative damping plus magnetic Jeans suppression) and feeding it into the existing excursion-set halo mass function and mean-field radiative-transfer modules produces reliable shifts in star-formation rate density, Lyman-alpha coupling, and 21-cm observables. No quantitative test of this mapping is shown for M_halo ~ 10^6-10^8 M_sun at z ~ 15-25, where non-linear and baryonic effects are expected to be important.

Authors: We acknowledge that the implementation relies on modifying the linear power spectrum and propagating it through zeus21's existing excursion-set and mean-field modules without dedicated new simulations for validation at these halo masses and redshifts. This follows the standard semi-numerical methodology used in codes like 21cmFAST for exploring enhanced small-scale power (e.g., in warm dark matter or primordial non-Gaussianity studies). The relative enhancement from PMFs is captured at linear order, with absolute normalization tied to the no-PMF baseline. In the revised manuscript we have added a dedicated paragraph in §3.2 discussing expected uncertainties from non-linear collapse and baryonic feedback, citing available PMF simulation literature, and explicitly noting that full hydrodynamical validation lies beyond the current scope. revision: partial
Referee: [§4] §4 (Forecasts and detectability): the claimed complementarity with CMB priors and the projected HERA/SKA constraints are derived directly from the unvalidated zeus21+PMF signals. Without an assessment of systematic uncertainty arising from the linear-P(k) approximation, the forecasted error bars and detection thresholds cannot be taken at face value.

Authors: We agree that systematic uncertainties from the linear approximation should be assessed before the forecasts can be interpreted at face value. The revised §4 now includes a qualitative discussion of these systematics, emphasizing that the dominant PMF signature is a timing shift in the 21-cm milestones rather than a change in fluctuation amplitude, and that the quoted detection thresholds are therefore conservative. The claimed complementarity with CMB priors is retained because 21-cm data probe the integrated small-scale structure-formation response (orthogonal to CMB damping constraints on larger scales), but we have clarified throughout the text that the numerical constraints are model-dependent and indicative within the adopted framework. revision: partial

standing simulated objections not resolved

Direct quantitative validation of the PMF-augmented halo mass function and 21-cm signals against N-body or hydrodynamical simulations that include non-linear gravitational collapse and baryonic physics at z~15-25 and M_halo~10^6-10^8 M_sun.

Circularity Check

0 steps flagged

No significant circularity; forecasts are forward predictions from an extended physical model

full rationale

The paper extends the zeus21 framework by adding a physically motivated PMF term to the linear matter power spectrum (with radiative damping and magnetic Jeans suppression). This is presented as an implementation choice, not a fit to the target 21-cm data. The forecasts for HERA/SKA detectability and combined CMB constraints are generated by propagating this modified P(k) through the existing zeus21 modules for halo abundance and radiative processes. No equations or steps in the provided text reduce the claimed results to fitted parameters, self-citations that bear the central load, or definitions that presuppose the output. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard cosmological assumptions plus the specific modeling choices for PMF damping and suppression; no new entities are postulated.

free parameters (1)

magnetic field amplitude
Fiducial values are explored across a range; the amplitude is a free parameter of the PMF model.

axioms (1)

domain assumption Standard Lambda-CDM background cosmology with added PMF contribution to linear power spectrum
Invoked when extending zeus21 to include radiative damping and magnetic Jeans suppression.

pith-pipeline@v0.9.0 · 5515 in / 1339 out tokens · 57674 ms · 2026-05-08T16:14:21.657184+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

71 extracted references · 58 canonical work pages · 2 internal anchors

[1]

Loeb and M

A. Loeb and M. Zaldarriaga, Measuring the small - scale power spectrum of cosmic density fluctuations through 21 cm tomography prior to the epoch of structure for- mation, Phys. Rev. Lett.92, 211301 (2004), arXiv:astro- ph/0312134

work page arXiv 2004
[2]

Barkana and A

R. Barkana and A. Loeb, A Method for separating the physics from the astrophysics of high-redshift 21 cm fluctuations, Astrophys. J. Lett.624, L65 (2005), arXiv:astro-ph/0409572

work page arXiv 2005
[3]

Furlanetto, S

S. Furlanetto, S. P. Oh, and F. Briggs, Cosmology at Low Frequencies: The 21 cm Transition and the High-Redshift Universe, Phys. Rept.433, 181 (2006), arXiv:astro- ph/0608032

work page arXiv 2006
[4]

J. R. Pritchard and A. Loeb, 21-cm cosmology, Rept. Prog. Phys.75, 086901 (2012), arXiv:1109.6012 [astro- ph.CO]

work page Pith review arXiv 2012
[5]

L. V. E. Koopmanset al., The Cosmic Dawn and Epoch of Reionization with the Square Kilometre Array, PoSAASKA14, 001 (2015), arXiv:1505.07568 [astro- ph.CO]

work page arXiv 2015
[6]

Fragoset al., X-ray Binary Evolution Across Cos- mic Time, Astrophys

T. Fragoset al., X-ray Binary Evolution Across Cos- mic Time, Astrophys. J.764, 41 (2013), arXiv:1206.2395 [astro-ph.HE]

work page arXiv 2013
[7]

Fragos, B

T. Fragos, B. D. Lehmer, S. Naoz, A. Zezas, and A. R. Basu-Zych, Energy Feedback from X-ray Binaries in the Early Universe, Astrophys. J. Lett.776, L31 (2013), arXiv:1306.1405 [astro-ph.CO]

work page arXiv 2013
[8]

Reionization and the Cosmic Dawn with the Square Kilometre Array

G. Mellemaet al., Reionization and the Cosmic Dawn with the Square Kilometre Array, Exper. Astron.36, 235 (2013), arXiv:1210.0197 [astro-ph.CO]

work page Pith review arXiv 2013
[9]

A. R. Parsons, J. C. Pober, J. E. Aguirre, C. L. Carilli, D. C. Jacobs, and D. F. Moore, A per-baseline, delay- spectrum technique for accessing the 21 cm cosmic reion- ization signature, The Astrophysical Journal756, 165 (2012)

2012
[10]

D. R. DeBoeret al., Hydrogen Epoch of Reionization Ar- ray (HERA), Publ. Astron. Soc. Pac.129, 045001 (2017), arXiv:1606.07473 [astro-ph.IM]

work page arXiv 2017
[11]

Tashiro and N

H. Tashiro and N. Sugiyama, The early reionization with the primordial magnetic fields, Mon. Not. Roy. Astron. Soc.368, 965 (2006), arXiv:astro-ph/0512626

work page arXiv 2006
[12]

Fialkov and R

A. Fialkov and R. Barkana, The rich complexity of 21-cm fluctuations produced by the first stars, Mon. Not. Roy. Astron. Soc.445, 213 (2014), arXiv:1409.3992 [astro- ph.CO]

work page arXiv 2014
[13]

K. E. Kunze, 21 cm line signal from magnetic modes, JCAP01, 033, arXiv:1805.10943 [astro-ph.CO]

work page arXiv
[14]

P. P. Kronberg, Extragalactic magnetic fields, Reports on Progress in Physics57, 325 (1994)

1994
[15]

T. E. Clarke, P. P. Kronberg, and H. Boehringer, A New radio - X-ray probe of galaxy cluster magnetic fields, Astrophys. J. Lett.547, L111 (2001), arXiv:astro- ph/0011281

work page arXiv 2001
[16]

Govoni and L

F. Govoni and L. Feretti, Magnetic field in clusters of galaxies, Int. J. Mod. Phys. D13, 1549 (2004), arXiv:astro-ph/0410182

work page arXiv 2004
[17]

Neronov and I

A. Neronov and I. Vovk, Evidence for strong extragalac- tic magnetic fields from fermi observations of tev blazars, Science328, 73 (2010)

2010
[18]

A. M. Taylor, I. Vovk, and A. Neronov, Extragalactic magnetic fields constraints from simultaneous gev–tev observations of blazars, Astronomy & Astrophysics529, A144 (2011)

2011
[19]

Beck and R

R. Beck and R. Wielebinski, Magnetic fields in galaxies, inPlanets, Stars & Stellar Systems, Vol. 5, edited by T. D. Oswalt and G. Gilmore (Springer Dordrecht, 2013) pp. 641–671

2013
[20]

Grasso and H

D. Grasso and H. R. Rubinstein, Magnetic fields in the early universe, Phys. Rept.348, 163 (2001), arXiv:astro- ph/0009061

work page arXiv 2001
[21]

L. M. Widrow, Origin of galactic and extragalactic mag- netic fields, Rev. Mod. Phys.74, 775 (2002), arXiv:astro- ph/0207240

work page arXiv 2002
[22]

Primordial magnetogenesis

A. Kandus, K. E. Kunze, and C. G. Tsagas, Pri- mordial magnetogenesis, Phys. Rept.505, 1 (2011), arXiv:1007.3891 [astro-ph.CO]

work page Pith review arXiv 2011
[23]

Cosmological Magnetic Fields: Their Generation, Evolution and Observation

R. Durrer and A. Neronov, Cosmological Magnetic Fields: Their Generation, Evolution and Observation, Astron. Astrophys. Rev.21, 62 (2013), arXiv:1303.7121 [astro-ph.CO]

work page Pith review arXiv 2013
[24]

The origin, evolution and signatures of primordial magnetic fields

K. Subramanian, The origin, evolution and signatures of primordial magnetic fields, Rept. Prog. Phys.79, 076901 (2016), arXiv:1504.02311 [astro-ph.CO]

work page Pith review arXiv 2016
[25]

Vachaspati, Progress on cosmological magnetic fields, Rept

T. Vachaspati, Progress on cosmological magnetic fields, Rept. Prog. Phys.84, 074901 (2021), arXiv:2010.10525 [astro-ph.CO]

work page arXiv 2021
[26]

Kahniashvili, Y

T. Kahniashvili, Y. Maravin, and A. Kosowsky, Fara- day rotation limits on a primordial magnetic field from Wilkinson Microwave Anisotropy Probe five-year data, Phys. Rev. D80, 023009 (2009), arXiv:0806.1876 [astro- ph]

work page arXiv 2009
[27]

P. A. R. Adeet al.(Planck), Planck 2015 results. XIX. Constraints on primordial magnetic fields, Astron. Astro- phys.594, A19 (2016), arXiv:1502.01594 [astro-ph.CO]

work page Pith review arXiv 2015
[28]

Jedamzik and A

K. Jedamzik and A. Saveliev, Stringent Limit on Primor- dial Magnetic Fields from the Cosmic Microwave Back- ground Radiation, Phys. Rev. Lett.123, 021301 (2019), arXiv:1804.06115 [astro-ph.CO]

work page arXiv 2019
[29]

Paoletti and F

D. Paoletti and F. Finelli, Constraints on primordial magnetic fields from magnetically-induced perturbations: current status and future perspectives with LiteBIRD and future ground based experiments, JCAP11, 028, arXiv:1910.07456 [astro-ph.CO]

work page arXiv 1910
[30]

Paoletti, J

D. Paoletti, J. Chluba, F. Finelli, and J. A. Rubi˜ no- Martin, Constraints on primordial magnetic fields from their impact on the ionization history with Planck 2018, Mon. Not. Roy. Astron. Soc.517, 3916 (2022), 12 arXiv:2204.06302 [astro-ph.CO]

work page arXiv 2018
[31]

K. E. Kunze and E. Komatsu, Constraints on primor- dial magnetic fields from the optical depth of the cosmic microwave background, JCAP06, 027, arXiv:1501.00142 [astro-ph.CO]

work page arXiv
[32]

Minoda, S

T. Minoda, S. Saga, T. Takahashi, H. Tashiro, D. Yamauchi, S. Yokoyama, and S. Yoshiura, Probing the primordial universe with 21-cm line from cosmic dawn/epoch of reionization, Publications of the Astro- nomical Society of Japan75, S154 (2022)

2022
[33]

Venumadhav, A

T. Venumadhav, A. Oklopcic, V. Gluscevic, A. Mishra, and C. M. Hirata, New probe of magnetic fields in the prereionization epoch. I. Formalism, Phys. Rev. D95, 083010 (2017), arXiv:1410.2250 [astro-ph.CO]

work page arXiv 2017
[34]

Gluscevic, T

V. Gluscevic, T. Venumadhav, X. Fang, C. Hirata, A. Oklopcic, and A. Mishra, New probe of magnetic fields in the pre-reionization epoch. II. Detectability, Phys. Rev. D95, 083011 (2017), arXiv:1604.06327 [astro- ph.CO]

work page arXiv 2017
[35]

Wasserman, On the origins of galaxies, galactic angu- lar momenta, and galactic magnetic fields, Astrophysical Journal224, 337 (1978)

I. Wasserman, On the origins of galaxies, galactic angu- lar momenta, and galactic magnetic fields, Astrophysical Journal224, 337 (1978)

1978
[36]

N. Y. Gnedin, Effect of reionization on the structure for- mation in the universe, Astrophys. J.542, 535 (2000), arXiv:astro-ph/0002151

work page arXiv 2000
[37]

S. K. Sethi and K. Subramanian, Primordial magnetic fields in the post-recombination era and early reion- ization, Mon. Not. Roy. Astron. Soc.356, 778 (2005), arXiv:astro-ph/0405413

work page arXiv 2005
[38]

S. K. Sethi, B. B. Nath, and K. Subramanian, Primor- dial magnetic fields and formation of molecular hydro- gen, Mon. Not. Roy. Astron. Soc.387, 1589 (2008), arXiv:0804.3473 [astro-ph]

work page Pith review arXiv 2008
[39]

D. G. Yamazaki, K. Ichiki, T. Kajino, and G. J. Math- ews, New Constraints on the Primordial Magnetic Field, Phys. Rev. D81, 023008 (2010), arXiv:1001.2012 [astro- ph.CO]

work page arXiv 2010
[40]

D. R. G. Schleicher, R. Banerjee, S. Sur, T. G. Arshakian, R. S. Klessen, R. Beck, and M. Spaans, Small-scale dy- namo action during the formation of the first stars and galaxies: I. the ideal mhd limit, Astronomy & Astro- physics522, A115 (2010)

2010
[41]

K. L. Pandey and S. K. Sethi, Probing primordial mag- netic fields using lyαclouds, The Astrophysical Journal 762, 15 (2012)

2012
[42]

K. L. Pandey, T. R. Choudhury, S. K. Sethi, and A. Fer- rara, Reionization constraints on primordial magnetic fields, Mon. Not. Roy. Astron. Soc.451, 1692 (2015), arXiv:1410.0368 [astro-ph.CO]

work page arXiv 2015
[43]

D. R. G. Schleicher and F. Miniati, Primordial magnetic field constraints from the end of reionization, Monthly Notices of the Royal Astronomical Society: Letters418, L143 (2011)

2011
[44]

Miralda-Escude, The dark age of the universe, Science 300, 1904 (2003), arXiv:astro-ph/0307396

J. Miralda-Escude, The dark age of the universe, Science 300, 1904 (2003), arXiv:astro-ph/0307396

work page arXiv 1904
[45]

D. Ryu, H. Kang, J. Cho, and S. Das, Turbulence and Magnetic Fields in the Large Scale Structure of the Uni- verse, Science320, 909 (2008), arXiv:0805.2466 [astro- ph]

work page arXiv 2008
[46]

Dubois and R

Y. Dubois and R. Teyssier, Cosmological MHD simula- tion of a cooling flow cluster, Astron. Astrophys.482, L13 (2008), arXiv:0802.0490 [astro-ph]

work page arXiv 2008
[47]

Marinacci, M

F. Marinacci, M. Vogelsberger, P. Mocz, and R. Pak- mor, The large-scale properties of simulated cosmological magnetic fields, Mon. Not. Roy. Astron. Soc.453, 3999 (2015), arXiv:1506.00005 [astro-ph.CO]

work page arXiv 2015
[48]

J. B. Mu˜ noz, An effective model for the cosmic-dawn 21- cm signal, Mon. Not. Roy. Astron. Soc.523, 2587 (2023), arXiv:2302.08506 [astro-ph.CO]

work page arXiv 2023
[49]

H. A. G. Cruz, J. B. Munoz, N. Sabti, and M. Kamionkowski, Effective model for the 21-cm sig- nal with population III stars, Phys. Rev. D111, 083503 (2025), arXiv:2407.18294 [astro-ph.CO]

work page arXiv 2025
[50]

H. A. G. Cruz, T. Adi, J. Flitter, M. Kamionkowski, and E. D. Kovetz, 21-cm fluctuations from primor- dial magnetic fields, Phys. Rev. D109, 023518 (2024), arXiv:2308.04483 [astro-ph.CO]

work page arXiv 2024
[51]

T. Adi, H. A. G. Cruz, and M. Kamionkowski, Primordial density perturbations from magnetic fields, Phys. Rev. D 108, 023521 (2023), arXiv:2306.11319 [astro-ph.CO]

work page arXiv 2023
[52]

E.-j. Kim, A. Olinto, and R. Rosner, Generation of den- sity perturbations by primordial magnetic fields, Astro- phys. J.468, 28 (1996), arXiv:astro-ph/9412070

work page arXiv 1996
[53]

Jedamzik, V

K. Jedamzik, V. c. v. Katalini´ c, and A. V. Olinto, Damp- ing of cosmic magnetic fields, Phys. Rev. D57, 3264 (1998)

1998
[54]

Subramanian and J

K. Subramanian and J. D. Barrow, Magnetohydrody- namics in the early universe and the damping of nonlinear alfv´ en waves, Phys. Rev. D58, 083502 (1998)

1998
[55]

Kahniashvili, A

T. Kahniashvili, A. G. Tevzadze, and B. Ratra, Phase Transition Generated Cosmological Magnetic Field at Large Scales, Astrophys. J.726, 78 (2011), arXiv:0907.0197 [astro-ph.CO]

work page arXiv 2011
[56]

The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview

J. Lesgourgues, The cosmic linear anisotropy solving system (class) i: Overview (2011), arXiv:1104.2932, arXiv:1104.2932 [astro-ph.IM]

work page Pith review arXiv 2011
[57]

D. Blas, J. Lesgourgues, and T. Tram, The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes, JCAP07, 034, arXiv:1104.2933 [astro-ph.CO]

work page internal anchor Pith review arXiv
[58]

The Cosmic Linear Anisotropy Solving System ( CLASS) III: Comparison with CAMB for LambdaCDM,

J. Lesgourgues, The cosmic linear anisotropy solving sys- tem (class) iii: Comparison with camb forλcdm (2011), arXiv:1104.2934, arXiv:1104.2934 [astro-ph.CO]

work page arXiv 2011
[59]

The Cosmic Linear Anisotropy Solving System (CLASS) IV: eﬃcient implementation of non-cold relics,

J. Lesgourgues and T. Tram, The Cosmic Lin- ear Anisotropy Solving System (CLASS) IV: efficient implementation of non-cold relics, JCAP09, 032, arXiv:1104.2935 [astro-ph.CO]

work page arXiv
[60]

R. K. Sheth and G. Tormen, Large scale bias and the peak background split, Mon. Not. Roy. Astron. Soc.308, 119 (1999), arXiv:astro-ph/9901122

work page Pith review arXiv 1999
[61]

Mesinger, S

A. Mesinger, S. Furlanetto, and R. Cen, 21cmfast: a fast, seminumerical simulation of the high-redshift 21-cm sig- nal: 21cmfast, Monthly Notices of the Royal Astronomi- cal Society411, 955 (2010)

2010
[62]

C. A. Watkinson, S. K. Giri, H. E. Ross, K. L. Dixon, I. T. Iliev, G. Mellema, and J. R. Pritchard, The 21-cm bispectrum as a probe of non-Gaussianities due to X-ray heating, Mon. Not. Roy. Astron. Soc.482, 2653 (2019), arXiv:1808.02372 [astro-ph.CO]

work page arXiv 2019
[63]

Bromm, Formation of the First Stars, Rept

V. Bromm, Formation of the First Stars, Rept. Prog. Phys.76, 112901 (2013), arXiv:1305.5178 [astro-ph.CO]

work page arXiv 2013
[64]

Fialkov, R

A. Fialkov, R. Barkana, and E. Visbal, The observable signature of late heating of the Universe during cosmic reionization, Nature506, 197 (2014), arXiv:1402.0940 [astro-ph.CO]

work page arXiv 2014
[65]

J. C. Pober, A. R. Parsons, D. R. DeBoer, P. McDon- ald, M. McQuinn, J. E. Aguirre, Z. Ali, R. F. Bradley, T.-C. Chang, and M. F. Morales, The Baryon Acoustic Oscillation Broadband and Broad-beam Array: Design 13 Overview and Sensitivity Forecasts, Astron. J.145, 65 (2013), arXiv:1210.2413 [astro-ph.CO]

work page arXiv 2013
[66]

J. C. Poberet al., What Next-Generation 21 cm Power Spectrum Measurements Can Teach Us About the Epoch of Reionization, Astrophys. J.782, 66 (2014), arXiv:1310.7031 [astro-ph.CO]

work page arXiv 2014
[67]

Planck 2018 results. VI. Cosmological parameters

N. Aghanimet al.(Planck), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

work page internal anchor Pith review arXiv 2018
[68]

Ciardi, A

B. Ciardi, A. Ferrara, and S. D. M. White, Early reion- ization by the first galaxies, Mon. Not. Roy. Astron. Soc. 344, L7 (2003), arXiv:astro-ph/0302451

work page arXiv 2003
[69]

N. Y. Gnedin, A. V. Kravtsov, and H.-W. Chen, Escape of Ionizing Radiation from High Redshift Galaxies, As- trophys. J.672, 765 (2008), arXiv:0707.0879 [astro-ph]

work page arXiv 2008
[70]

Kuhlen and C

M. Kuhlen and C. A. Faucher-Giguere, Concordance models of reionization: implications for faint galaxies and escape fraction evolution, Mon. Not. Roy. Astron. Soc. 423, 862 (2012), arXiv:1201.0757 [astro-ph.CO]

work page arXiv 2012
[71]

J. H. Wise, V. G. Demchenko, M. T. Halicek, M. L. Nor- man, M. J. Turk, T. Abel, and B. D. Smith, The birth of a galaxy – III. Propelling reionization with the faintest galaxies, Mon. Not. Roy. Astron. Soc.442, 2560 (2014), arXiv:1403.6123 [astro-ph.CO]. 14 Appendix A: F ull Fisher Constraint T ables This appendix collects the full marginalized 1σconstrai...

work page arXiv 2014