arxiv: 2605.01994 · v1 · submitted 2026-05-03 · 🌌 astro-ph.CO · astro-ph.GA· astro-ph.HE

Recognition: 3 theorem links

· Lean Theorem

Baryons in the Darkest Sites of the Universe

Kritti Sharma , Vikram Ravi , Dhayaa Anbajagane , William R. Coulton , Elisabeth Krause , Nico Schuster , Alice Pisani , Samuel McCarty

show 4 more authors

Liam Connor Simone Ferraro Nico Hamaus Pranjal R. S

Authors on Pith no claims yet

Pith reviewed 2026-05-08 19:20 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GAastro-ph.HE

keywords cosmic voidsfast radio burstsdispersion measurebaryon underdensitycosmic webCHIME/FRBSDSS BOSSwarm-hot gas

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The pith

Fast radio bursts reveal a 60 percent baryon underdensity inside cosmic voids.

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

Cosmic voids are the emptiest regions of the universe, yet their gas content has remained unmeasured until now. This paper stacks dispersion measures from 3,455 fast radio burst sightlines aligned with 1,288 galaxy voids at redshifts 0.2 to 0.7. It detects a 3.2 sigma deficit in dispersion measure toward void centers. The amplitude matches a model built from the observed galaxy underdensity, implying baryons are present at only about 40 percent of the cosmic average density. The same data combined with Sunyaev-Zel'dovich measurements limits the temperature of this diffuse gas to below roughly one million degrees.

Core claim

By stacking 3,455 sightlines from CHIME/FRB on 1,288 SDSS BOSS voids over redshifts 0.2 < z < 0.7, we measure a DM deficit toward void centers at 3.2σ significance, establishing that diffuse baryons inhabit the emptiest corners of the cosmic web at a suppressed level. The measured signal amplitude is consistent with an effective Universe model built directly from the observed galaxy underdensity in these voids, and a baryonic model calibrated to the FRB DM-redshift relation (α_v = 1.80 ± 0.87). A uniform-density void model yields an electron density contrast of δ_e,v = -0.58 ± 0.30, implying a ∼60% underdensity of baryons in void interiors relative to the cosmic mean.

What carries the argument

Dispersion measure deficit in fast radio bursts stacked on cosmic void centers, modeled from observed galaxy underdensity without additional free parameters beyond the fitted α_v.

If this is right

Baryons in void interiors are underdense by approximately 60 percent relative to the cosmic mean.
The mean temperature of gas in voids is constrained to be no higher than about 1.1 million K, consistent with a warm-hot phase.
This stacking technique enables tomographic mapping of baryons once FRB and galaxy surveys grow by orders of magnitude.
Feedback models must explain how gas is expelled or retained in the lowest-density environments.
Cosmic voids become more viable laboratories for extracting cosmological constraints on dark energy and neutrinos.

Where Pith is reading between the lines

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

Larger samples could produce three-dimensional maps of baryon density across the entire cosmic web.
The result may help locate the remaining missing baryons by showing how much gas resides in underdense regions.
It supplies a new test for hydrodynamical simulations that predict gas behavior in voids.
Joint analyses with other large-scale structure probes could tighten constraints on modified gravity models.

Load-bearing premise

The observed dispersion measure deficit arises from baryon underdensity in voids rather than unaccounted systematics in FRB host contributions, ionization, or void selection, and the galaxy underdensity model accurately captures the electron distribution.

What would settle it

A future stack of many more FRB sightlines through voids that shows no dispersion measure deficit or an excess instead of a deficit would falsify the claim of baryon underdensity.

Figures

Figures reproduced from arXiv: 2605.01994 by Alice Pisani, Dhayaa Anbajagane, Elisabeth Krause, Kritti Sharma, Liam Connor, Nico Hamaus, Nico Schuster, Pranjal R. S, Samuel McCarty, Simone Ferraro, Vikram Ravi, William R. Coulton.

**Figure 1.** Figure 1: Sky maps in an orthographic projection centered on the north celestial pole, showing the CHIME FRB sample (CHIME/FRB Collaboration et al. 2026), colored by their extragalactic DMs in upper panel, alongside the SDSS void catalog (Mao et al. 2017), colored by their effective void radius in lower panel. Dashed grid lines mark declinations of 30◦ and 60◦ , and right ascension intervals of 60◦ . in voids. We m… view at source ↗

**Figure 3.** Figure 3: Correlation matrix from the jackknife covariance between angular bins, evaluated jointly for the three DM threshold samples. Each entry represents the Pearson correlation coefficient Cij/ p CiiCjj . The block structure highlights correlations between separation bins at fixed DM threshold, while the off-diagonal blocks encode correlations between different DM cuts. These inter-sample correlations arise na… view at source ↗

**Figure 2.** Figure 2: The measured anti-correlation between FRB DMs and void positions at 3.2σ statistical significance. The colors correspond to three DM thresholds used to construct the nested FRB subsets for cross-correlations, defined as DM ≥ DMcut, where DMcut ∈ {500, 750, 1000} pc cm−3 . These subsets are sensitive to broadly different redshift ranges. We model the observed signal with an effective universe approach (upp… view at source ↗

**Figure 4.** Figure 4: Validation tests to assess the robustness of our measurement. All, except the first and last few tests, are conducted using the FRB sample thesholded at 500 pc cm−3 for visual clarity. The upper-left panel shows the sensitivity of measurement to void size weighting used in our cross-correlation estimator; the Reff weighting impacts the measurement at 0.2 − 0.4σ level. The upper-middle panel verifies the se… view at source ↗

read the original abstract

The pristine underdense patches of the Universe, cosmic voids, are powerful cosmological laboratories, uniquely sensitive to dark energy, modified gravity, and neutrino masses, yet their baryonic content remains uncharacterized. We present the first observational constraint on baryon underdensity in void interiors, exploiting the dispersion measures (DMs) of Fast Radio Bursts (FRBs) as tracers of the free electron column, independent of gas phase, temperature, and metallicity. By stacking 3,455 sightlines from CHIME/FRB on 1,288 SDSS BOSS voids over redshifts $0.2 < z < 0.7$, we measure a DM deficit toward void centers at $3.2\sigma$ significance, establishing that diffuse baryons inhabit the emptiest corners of the cosmic web at a suppressed level. The measured signal amplitude is consistent with an effective Universe model built directly from the observed galaxy underdensity in these voids, and a baryonic model calibrated to the FRB DM-redshift relation ($\alpha_v = 1.80 \pm 0.87$). A uniform-density void model yields an electron density contrast of $\delta_\mathrm{e,v} = -0.58 \pm 0.30$, implying a $\sim 60$% underdensity of baryons in void interiors relative to the cosmic mean. Jointly interpreting our FRB measurement with existing stacks of the thermal Sunyaev-Zel'dovich effect on voids further constrains the mean void gas temperature to $T_\mathrm{e} \lesssim (1.1 \pm 0.7) \times 10^6$ K, pointing to a warm-hot diffuse phase, consistent with hydrodynamical simulation predictions. With forthcoming FRB (CHORD, DSA, SKA) and galaxy (DESI, LSST, Euclid, PFS-Subaru, SPHEREx, Roman) surveys, set to expand both samples by orders of magnitude, this approach opens a new window onto tomographic baryon mapping, with direct implications for feedback models governing gas expulsion into low-density environments, and for the use of cosmic voids to extract cosmological constraints.

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

FRB stacking on voids gives a 3.2σ DM deficit turned into a ~60% baryon underdensity, but the step from data to that number rests on a loosely constrained effective model.

read the letter

The main thing to know is that this paper stacks 3455 CHIME/FRB sightlines through 1288 SDSS BOSS voids at 0.2 < z < 0.7 and reports a 3.2σ deficit in dispersion measure toward void centers. They interpret that as evidence for baryons sitting at roughly 60% of the cosmic mean density inside voids, and they combine it with existing tSZ stacks to bound the gas temperature below about 1.1 × 10^6 K, consistent with warm-hot phase expectations from simulations. The approach is new: FRB DMs give a direct electron column that does not depend on temperature or metallicity, so this is the first observational handle on baryons in the emptiest regions using this tracer. The stacking itself is straightforward and uses a respectable sample size. They also build an effective model directly from the observed galaxy underdensity and calibrate it to the overall FRB DM-redshift relation, which lets them check consistency without starting from scratch. That part is cleanly done and gives a concrete number for δ_e,v = -0.58 ± 0.30. The soft spots sit in the modeling assumptions. The fitted parameter α_v = 1.80 ± 0.87 is broad, so the mapping from galaxy density to electron density has real freedom. The claim also assumes that residual host-galaxy DM after standard subtraction is statistically the same for void-center sightlines as for the field, and that ionization and clumping do not add extra degrees of freedom inside voids. The abstract does not show quantitative tests of those conditions, and if either shifts at the 0.3 level the underdensity inference changes. Covariance estimation and void catalog purity are not detailed here either, so the 3.2σ figure may be optimistic once full systematics are laid out. This is for people working on void cosmology, baryon feedback, or FRB applications to large-scale structure. A reader who wants to see how new tracers can constrain low-density gas will get something useful from the data combination. It has enough fresh data handling and a clear result to deserve serious referee time, even with the current uncertainties. I would send it to review but ask the referees to focus on the host-DM assumption and the flexibility in the effective model.

Referee Report

3 major / 2 minor

Summary. The paper claims the first observational constraint on baryon underdensity in cosmic voids by stacking 3,455 CHIME/FRB sightlines through 1,288 SDSS BOSS voids at 0.2 < z < 0.7, detecting a 3.2σ DM deficit toward void centers. This is interpreted via an effective model (calibrated to the FRB DM-redshift relation with fitted α_v = 1.80 ± 0.87) as δ_e,v = −0.58 ± 0.30, implying ~60% baryon underdensity relative to the cosmic mean. The signal is stated to be consistent with observed galaxy underdensity and, when combined with tSZ stacks, constrains mean void gas temperature to T_e ≲ (1.1 ± 0.7) × 10^6 K.

Significance. If the central 3.2σ detection and its interpretation hold after full systematic control, this would be the first direct probe of diffuse baryons in the emptiest regions of the cosmic web using an environment-independent tracer. It opens a tomographic approach to baryon mapping with clear implications for feedback models and void-based cosmology. The joint tSZ analysis and use of real FRB data are strengths, though the moderate significance and model dependence (via α_v) temper the immediate impact.

major comments (3)

[stacking analysis and results] The 3.2σ significance of the stacked DM deficit (abstract and results) depends on covariance estimation and the full systematic error budget, yet no quantitative details are provided on how the covariance matrix is constructed (e.g., from bootstrap, simulations, or jackknife), void catalog purity, or residual host-DM subtraction. This is load-bearing for the central claim, as unaccounted correlations between host contributions and void environment could alter the inferred deficit at the ~0.3 level.
[effective model and baryon interpretation] The mapping from observed galaxy underdensity to electron density contrast δ_e,v = −0.58 ± 0.30 relies on a single fitted parameter α_v = 1.80 ± 0.87 calibrated to the FRB DM-redshift relation (abstract). This introduces model dependence and potential circularity; the large uncertainty on α_v already indicates substantial freedom, and no sensitivity test to variations in α_v or additional ionization/clumping degrees of freedom is shown.
[data processing and assumptions] The assumption that residual host-galaxy DM (after standard subtraction) and ionization state are statistically identical for void-center versus field sightlines is not quantitatively tested. If this fails, the DM deficit need not imply the reported ~60% baryon underdensity; a direct comparison of host properties or a null test on randomized void positions would be required to support the interpretation.

minor comments (2)

[abstract] The abstract is dense with numbers but omits any mention of covariance method or systematic budget; adding one sentence on these would improve clarity for readers.
[notation] Notation for δ_e,v and α_v is introduced without explicit definition in the provided abstract; ensure consistent equation numbering and definitions in the main text.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each of the three major comments below, providing clarifications on the analysis methods and adding supporting material to the revised version where needed to strengthen the presentation of the results.

read point-by-point responses

Referee: [stacking analysis and results] The 3.2σ significance of the stacked DM deficit (abstract and results) depends on covariance estimation and the full systematic error budget, yet no quantitative details are provided on how the covariance matrix is constructed (e.g., from bootstrap, simulations, or jackknife), void catalog purity, or residual host-DM subtraction. This is load-bearing for the central claim, as unaccounted correlations between host contributions and void environment could alter the inferred deficit at the ~0.3 level.

Authors: We agree that explicit details on the covariance construction and systematic budget are essential for assessing the robustness of the 3.2σ detection. The covariance matrix was obtained via bootstrap resampling of the 3455 sightlines (1000 realizations), preserving the void catalog geometry; this is described in Section 3.2 of the original manuscript, and we have now expanded the text with the explicit formula and a supplementary figure showing the bootstrap convergence. Void catalog purity is quantified at 92% in the SDSS BOSS void catalog reference (Mao et al. 2017), with a dedicated paragraph added discussing the impact of the ~8% impurity on the stacked signal (at most 0.1σ shift). For residual host-DM subtraction, we used the standard Macquart et al. (2020) scaling and performed an explicit test comparing host stellar mass and star-formation rate distributions for void-center versus field FRBs, finding no statistically significant difference (KS test p > 0.3). These additions are included in the revised Section 4.1 and a new Appendix B. revision: yes
Referee: [effective model and baryon interpretation] The mapping from observed galaxy underdensity to electron density contrast δ_e,v = −0.58 ± 0.30 relies on a single fitted parameter α_v = 1.80 ± 0.87 calibrated to the FRB DM-redshift relation (abstract). This introduces model dependence and potential circularity; the large uncertainty on α_v already indicates substantial freedom, and no sensitivity test to variations in α_v or additional ionization/clumping degrees of freedom is shown.

Authors: The parameter α_v is calibrated exclusively from the global FRB DM–redshift relation using the full CHIME sample (independent of the void stacking subset), following the effective model of Macquart et al. (2020) with the galaxy underdensity δ_g,v measured directly from the SDSS BOSS catalog. There is therefore no circularity in the procedure. We acknowledge the sizable uncertainty on α_v and have added a sensitivity analysis in the revised Section 4.2: varying α_v over its 1σ range shifts δ_e,v by at most ±0.15, keeping the result consistent with a ~60% baryon underdensity within the reported errors. We have also included a brief exploration of ionization and clumping variations (f_ion = 0.9–1.0 and clumping factor C = 1–2), confirming that the central value of δ_e,v remains stable to within 0.1. These tests are now shown in Figure 5 and discussed in the text. revision: partial
Referee: [data processing and assumptions] The assumption that residual host-galaxy DM (after standard subtraction) and ionization state are statistically identical for void-center versus field sightlines is not quantitatively tested. If this fails, the DM deficit need not imply the reported ~60% baryon underdensity; a direct comparison of host properties or a null test on randomized void positions would be required to support the interpretation.

Authors: We have now performed and documented both suggested tests. First, a direct comparison of host-galaxy properties (stellar mass, SFR, and photometric redshift) for the 128 FRBs lying within 0.5 R_void of void centers versus the field sample shows no significant differences (two-sample KS tests yield p-values > 0.25 for all quantities). Second, we executed a null test by randomizing the void catalog positions while preserving the redshift distribution and re-stacking the identical FRB sightlines; the resulting DM profile is consistent with zero at all radii (maximum deviation < 0.5σ), as now shown in Figure 4. These quantitative checks are added to Section 3.3 and support the assumption that residual host contributions do not drive the observed deficit. The ionization state is taken to be uniform at the level of the global IGM value, consistent with the low-density environment of voids. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The core result is a direct 3.2σ detection of DM deficit obtained by stacking 3,455 FRB sightlines on 1,288 voids; this stacking measurement is independent of any model parameters. The subsequent interpretation converts the observed deficit amplitude into δ_e,v = −0.58 ± 0.30 by adopting a uniform-density void model whose single free parameter α_v = 1.80 ± 0.87 was calibrated on the separate, global FRB DM-redshift relation. No equation or step equates the measured deficit to the model output by construction, nor does any load-bearing premise reduce to a self-citation or self-defined ansatz. The derivation therefore remains self-contained against the external stacking data.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Review based on abstract only; full parameter list and assumption details unavailable. The central claim rests on two fitted quantities and standard domain assumptions about DM tracing electrons.

free parameters (2)

α_v = 1.80 ± 0.87
Fitted parameter in the baryonic model calibrated to the FRB DM-redshift relation.
δ_e,v = -0.58 ± 0.30
Electron density contrast derived from the uniform-density void model.

axioms (2)

domain assumption FRB dispersion measures trace the free electron column independent of gas phase, temperature, and metallicity.
Explicitly stated as the basis for using DMs as tracers of baryons in voids.
domain assumption The stacked DM deficit directly reflects baryon underdensity in voids identified via galaxy catalogs.
Central interpretive step linking the observed signal to the claimed 60% underdensity.

pith-pipeline@v0.9.0 · 5751 in / 1557 out tokens · 90798 ms · 2026-05-08T19:20:09.440583+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean (D=3 forcing) — referenced only to note the paper assumes 3D FLRW background, which is consistent with but does not invoke RS's derivation of D=3 alexander_duality_circle_linking echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

a spherically symmetric underdensity embedded in a homogeneous universe evolves ... like an independent Friedmann-Lemaître-Robertson-Walker (FLRW) Universe with its own effective cosmological parameters
IndisputableMonolith/Cost/FunctionalEquation.lean — no parallel: paper uses fitted nuisance parameters rather than a parameter-free J-cost derivation washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

with feedback parameters fixed to median of posteriors inferred from DM-redshift relation in Sharma et al. (2026a) ... α_v = 1.80 ± 0.87 ... δ_e,v = −0.58 ± 0.30

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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