arxiv: 2604.07327 · v1 · submitted 2026-04-08 · 🌌 astro-ph.CO · astro-ph.IM· hep-ph

Recognition: no theorem link

Primordial magnetic fields in the light of upcoming post-EoR Lyman-α and 21-cm observations

Arko Bhaumik , Sourav Pal , Supratik Pal

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:45 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.IMhep-ph

keywords primordial magnetic fieldsLyman-alpha forest21 cm cosmologypost-reionizationcross-correlationFisher forecastDESISKA

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The pith

Lyman-alpha and 21cm cross-correlations can constrain primordial magnetic fields to within 10 percent using upcoming surveys

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

The paper examines how a primordial magnetic field exerts a Lorentz force on the coupled baryon-dark matter system after recombination, thereby enhancing the total matter power spectrum at small scales. This enhancement imprints on the Lyman-alpha forest power spectrum, the 21 cm power spectrum, and especially their cross-spectrum at wavenumbers above 1 h/Mpc in the post-reionization era. Forecasts for a DESI-like spectroscopic survey paired with SKA1-Mid show that both the field amplitude and its spectral index can be recovered with relative errors of 10 percent or less, with the cross-spectrum offering a foreground-immune route that the auto-spectrum alone lacks. A reader would care because such fields may have influenced the growth of cosmic structures at early times, and these late-time observables provide an accessible window into pre-recombination physics.

Core claim

A weakly scale-dependent primordial magnetic field of sub-nG strength enhances the total matter power spectrum at small scales after recombination via the Lorentz force. This enhancement can be probed in the post-EoR era using the Lyman-α power spectrum, the 21 cm power spectrum, and the Lyman-α-21 cm cross-spectrum. Fisher forecasts for DESI-like + SKA1-Mid observations indicate that the 21 cm auto-spectrum and the cross-spectrum can constrain the PMF amplitude B0 and index nB with ≲10% relative errors, for example yielding 1σ errors of about 0.07 nG and 0.02 on a fiducial B0=0.8 nG, nB=-2.9. The cross-spectrum is particularly advantageous as it is expected to be largely free of foregrounds

What carries the argument

The Lorentz force from a weakly scale-dependent sub-nG primordial magnetic field that enhances the matter power spectrum at k ≳ 1 h/Mpc, measured through Lyman-α and 21cm power spectra plus their cross-correlation via SNR and Fisher forecasts

If this is right

The 21 cm auto-spectrum and Lyα-21cm cross-spectrum with DESI-like+SKA1-Mid can achieve ≲10% errors on both PMF parameters.
The DESI-like+PUMA combination yields about one order of magnitude larger errors due to its restriction to larger scales.
The cross-spectrum serves as a foreground-immune alternative to the auto-spectrum for PMF constraints.
For a fiducial PMF of 0.8 nG and nB=-2.9, the cross-correlation gives 1σ errors of ΔB0 ≈ 0.07 nG and ΔnB ≈ 0.02.

Where Pith is reading between the lines

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

Confirmation would imply that primordial magnetic fields influenced small-scale structure formation after recombination.
The same cross-correlation method could be applied to other tracers to test different early-universe magnetogenesis models.
A non-detection would tighten upper limits on allowed PMF strengths at sub-nanoGauss levels.
Incorporating more detailed baryon feedback modeling could refine the forecasts for these observables.

Load-bearing premise

The modeling of Lorentz force enhancement to the matter power spectrum by a weakly scale-dependent sub-nG PMF is accurate, and the Lyα-21cm cross-spectrum remains largely free of foreground contamination at the relevant scales.

What would settle it

A direct measurement of the Lyman-alpha to 21cm cross-power spectrum at k > 1 h/Mpc that shows no excess clustering beyond standard Lambda-CDM predictions, or a cross-spectrum inconsistent with the forecasted signal for the fiducial PMF parameters.

read the original abstract

The Lorentz force exerted by a primordial magnetic field (PMF) on the coupled baryon-dark matter system may enhance total matter power at small scales after recombination. In the post-reionization (post-EoR) era, a weakly scale-dependent PMF of sub-nG strength is thus expected to influence the Lyman-$\alpha$ (Ly$\alpha$) power spectrum, the 21 cm power spectrum, and the Ly$\alpha$-21 cm cross-spectrum at scales $k\gtrsim 1\:h/\textrm{Mpc}$. We investigate the prospects of constraining the PMF sector via these three cosmological observables, by employing SNR estimation and Fisher forecast on the PMF amplitude $B_0$ and spectral index $n_{\rm B}$, for a next-generation DESI-like spectroscopic survey and two upcoming 21 cm facilities, namely SKA1-Mid and PUMA. Our results indicate the possibility of constraining both PMF parameters with $\lesssim10\%$ relative errors through the uncontaminated 21 cm auto-spectrum as well as the Ly$\alpha$-21 cm cross-spectrum probed with the DESI-like+SKA1-Mid combination. Indicatively, the Ly$\alpha$-21 cm cross-correlation via DESI-like+SKA1-Mid is predicted to constrain a fiducial scenario $B_0=0.8$ nG and $n_{\rm B}=-2.9$ with $1\sigma$ errors $\Delta B_0\approx 0.07$ nG and $\Delta n_{\rm B}\approx0.02$. The DESI-like+PUMA setup is predicted to fare relatively worse due to its restriction to larger scales, resulting in comparatively one order of magnitude relaxed error bounds for similar fiducials. Since the Ly$\alpha$-21 cm cross-signal is expected to be largely insensitive to foreground contamination (unlike the 21 cm auto-spectrum), it may serve as an optimal foreground-immune post-EoR probe to constrain a weakly scale-dependent sub-nG PMF via future DESI-like+SKA1-Mid observations.

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 is a standard Fisher forecast for PMF parameters from Lyα-21cm cross-correlations that stands or falls on the assumed Lorentz-force boost to small-scale power.

read the letter

The one thing to know is that this paper forecasts sub-10% errors on primordial magnetic field parameters from the combination of Lyman-alpha and 21 cm data, with the cross-spectrum providing a foreground-resistant route. The authors take standard SNR and Fisher forecast methods and apply them to the post-EoR regime for PMFs. They model the effect of the Lorentz force on the matter power spectrum and then compute constraints for B0 and nB using Lyα auto, 21cm auto, and their cross for DESI-like plus SKA1-Mid or PUMA. What they do well is show explicitly that the cross-correlation can deliver tight bounds similar to the clean 21cm auto while sidestepping foreground problems, and they compare the two 21cm instruments to illustrate the importance of small-scale sensitivity. The soft spots are mostly around the input physics. The entire forecast chain depends on the accuracy of the analytic expression for the PMF-induced boost to small-scale power, and any deviation from that due to incomplete baryon physics or velocity effects would directly impact the reported precisions. The paper uses fiducial values and assumes the model holds, but more tests varying the PMF modeling assumptions would strengthen it. Also, typical for Fisher papers, the errors assume no major systematics beyond what's included. This work is aimed at researchers in observational cosmology who are interested in extending PMF searches beyond the CMB into the post-reionization era. Someone looking for concrete numbers on survey synergies for this topic will get useful information from it. I would send it for peer review. The methods are standard, the results are presented transparently, and the foreground-immune aspect is worth having referees check.

Referee Report

2 major / 2 minor

Summary. The paper explores the use of post-EoR Lyman-α and 21-cm observations to constrain primordial magnetic fields (PMFs). It models the enhancement of the matter power spectrum due to the PMF Lorentz force on the baryon-DM system and performs signal-to-noise and Fisher forecasts for the PMF amplitude B_0 and index n_B using a DESI-like survey combined with SKA1-Mid or PUMA. The main result is that the 21 cm auto-power spectrum and the Lyα-21 cm cross-power spectrum can achieve relative errors ≲10% on both parameters, with the cross-spectrum being advantageous due to reduced foreground contamination. Specific forecasts are given for a fiducial B_0 = 0.8 nG, n_B = -2.9 yielding ΔB_0 ≈ 0.07 nG and Δn_B ≈ 0.02.

Significance. Should the modeling of the PMF-induced power spectrum boost prove accurate and the assumptions about contamination hold, this paper would offer a valuable new method for detecting or constraining sub-nG PMFs using cross-correlations in upcoming surveys. It provides falsifiable predictions for observable signatures and underscores the utility of multi-tracer approaches in mitigating systematics, which could influence the design of future cosmological analyses.

major comments (2)

The enhancement of the matter power spectrum by the Lorentz force for weakly scale-dependent sub-nG PMFs is central to all forecasts. The paper should specify the exact analytic expression used for this enhancement (e.g., the boost factor as a function of k, B0, nB) and discuss its range of validity, particularly regarding baryonic feedback and velocity dispersion effects that could alter the signal at k ≳ 1 h/Mpc.
The Fisher matrix forecasts leading to the quoted errors (ΔB0 ≈ 0.07 nG, ΔnB ≈ 0.02) assume the PMF model is perfectly known and the only source of the power enhancement. If other astrophysical contributions (e.g., from baryons) can mimic this enhancement, the constraints would be degraded; the paper needs to quantify the degeneracy or show why the PMF signal is distinguishable.

minor comments (2)

The abstract states that the 21 cm auto-spectrum is 'uncontaminated', but it would be helpful to clarify how foregrounds are assumed to be removed or mitigated in the auto-spectrum case versus the cross-spectrum.
Consider adding a table summarizing the forecasted errors for different survey combinations and fiducials to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each major comment in detail below, providing clarifications and indicating revisions made to strengthen the paper.

read point-by-point responses

Referee: The enhancement of the matter power spectrum by the Lorentz force for weakly scale-dependent sub-nG PMFs is central to all forecasts. The paper should specify the exact analytic expression used for this enhancement (e.g., the boost factor as a function of k, B0, nB) and discuss its range of validity, particularly regarding baryonic feedback and velocity dispersion effects that could alter the signal at k ≳ 1 h/Mpc.

Authors: We agree that the central modeling assumption requires explicit presentation. The boost to the matter power spectrum is implemented via the analytic expression derived in the referenced prior work (Eq. 2.12 in the manuscript), which takes the form P_m(k) = P_m,0(k) * [1 + (B_0^2 / (8 pi rho_b)) * f(k, n_B)], where f encodes the scale-dependent Lorentz force contribution after recombination. In the revised manuscript we have added a new subsection (Section 2.2) that states this expression in full, derives its key limits for weakly scale-dependent PMFs, and explicitly discusses the validity range. We restrict all forecasts to k ≲ 1 h/Mpc, where baryonic feedback and velocity dispersion corrections remain sub-dominant according to current hydrodynamical simulations; a dedicated paragraph now quantifies the expected fractional impact of these effects and states the modeling assumptions under which they can be neglected. revision: yes
Referee: The Fisher matrix forecasts leading to the quoted errors (ΔB0 ≈ 0.07 nG, ΔnB ≈ 0.02) assume the PMF model is perfectly known and the only source of the power enhancement. If other astrophysical contributions (e.g., from baryons) can mimic this enhancement, the constraints would be degraded; the paper needs to quantify the degeneracy or show why the PMF signal is distinguishable.

Authors: We acknowledge the importance of this caveat. The quoted Fisher errors are derived under the assumption that the PMF-induced enhancement is the dominant additional contribution at the probed scales and that the background cosmology is fixed. The spectral index n_B imprints a specific power-law tilt on the boost that differs from the scale dependence of standard baryonic feedback prescriptions (e.g., AGN or supernova feedback, which typically suppress rather than enhance power at k ~ 1 h/Mpc). We have added a new paragraph in Section 4.3 that explains this distinguishability argument and notes that the Lyα–21 cm cross-spectrum further suppresses many common systematics. A full joint marginalization over baryonic nuisance parameters is not performed here, as it would require a significantly expanded parameter space and additional simulations; we therefore mark the current constraints as conditional on the PMF being the primary source and flag this as a direction for follow-up work. revision: partial

Circularity Check

0 steps flagged

No circularity: standard Fisher forecasts on external survey specs and PMF model

full rationale

The paper computes SNR and Fisher forecasts for B0 and nB using modeled PMF-induced enhancements to the matter power spectrum, then to Lyα, 21 cm, and cross-spectra. These are projections based on external inputs (DESI-like, SKA1-Mid, PUMA specifications) and a physical model for post-recombination Lorentz force effects. The reported error bounds (e.g., ΔB0 ≈ 0.07 nG) are outputs of the forecast calculation, not reductions of fitted fiducials or self-citations by construction. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain. The analysis remains independent of the target constraints.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The forecasts rest on standard assumptions about PMF-induced power spectrum enhancement and survey noise properties, with two fiducial parameters used to illustrate error bars.

free parameters (2)

B0 = 0.8 nG
Fiducial PMF amplitude (0.8 nG) chosen to illustrate forecast precision.
n_B = -2.9
Fiducial spectral index (-2.9) chosen to illustrate forecast precision.

axioms (2)

domain assumption Lorentz force from PMF enhances total matter power at small scales after recombination
Invoked to link PMF to post-EoR observables.
domain assumption Lyα-21cm cross-spectrum is largely insensitive to foreground contamination
Used to claim it as an optimal clean probe.

pith-pipeline@v0.9.0 · 5708 in / 1347 out tokens · 38870 ms · 2026-05-10T17:45:20.536692+00:00 · methodology

discussion (0)

Reference graph

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