Gigaparsec structures are nowhere to be seen in $\Lambda$CDM: an enhanced analysis of LSS in FLAMINGO-10K simulations

A.M Lopez; R.G. Clowes

REVIEW 4 major objections 6 minor 2 cited by

Gigaparsec structures are nowhere to be seen in $\Lambda$CDM: an enhanced analysis of LSS in FLAMINGO-10K simulations

T0 review · 4 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Using the full FLAMINGO-10K simulation box and an enhanced statistical analysis, this paper finds no gigaparsec-scale structures and only a few ultra-large structures, leaving the Giant Arc and Big Ring as significant challenges to…

desk verdict A credible reanalysis that corrects Sawala et al.'s linkage scale, but its grand conclusion about the Giant Arc rests on an untested tracer assumption. read the letter →

arxiv 2504.14940 v1 pith:XLJLMUHN submitted 2025-04-21 astro-ph.CO

A.M Lopez , R.G. Clowes This is my paper · ORCID

classification astro-ph.CO

keywords GiantArcBigRinglarge-scalestructureLambda-CDMFLAMINGO-10KsimulationFriends-of-Friends/MSTalgorithmPoissonpointdistributioncosmologicalprinciple

open problems Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper re-examines the FLAMINGO-10K cosmological simulation to test whether the ~1 gigaparsec Giant Arc, seen in magnesium-II absorbers at $z \sim 0.8$, can be produced by a standard $\Lambda$CDM universe. Using the full $2.8^3$ Gpc$^3$ box, subhaloes at $z=0.7$, and 100 random realisations, the authors apply three clustering algorithms with a linkage scale appropriate to simulated data and find no gigaparsec structures, only a few ultra-large structures, and a large-scale distribution that is statistically indistinguishable from a Poisson point distribution. The paper argues that a prior claim of abundant gigaparsec patterns rested on an inappropriate linkage scale and a missing independent significance test. If correct, the Giant Arc and the nearby Big Ring remain statistically significant departures from $\Lambda$CDM, presenting a more direct challenge to the standard cosmological model.

What carries the argument

The load-bearing object is the linkage scale in the Single-Linkage Hierarchical Clustering (SLHC) / Friends-of-Friends algorithm, which decides which points belong to one structure. For simulated data with exact coordinates, the paper uses the mean nearest-neighbour separation for a Poisson distribution, $\bar{r} \approx 0.55(1/\rho)^{1/3}$, giving $65$ Mpc for the FLAMINGO-10K subhalo density, rather than the $95$ Mpc that had been used for real MgII data, a value that includes allowances for redshift errors, peculiar velocities, and gaps in background probes. Around this choice, the paper applies three algorithms, SLHC, the Convex Hull of Member Spheres (CHMS), which builds the convex hull of spheres of fixed radius around each member to estimate significance, and the Minimal Spanning Tree (MST) method, and compares candidate structures with 100 random realisations and with random Poisson data.

What would settle it

A hydrodynamical simulation of the same volume that predicts MgII absorption directly from the gas distribution (for example, via photoionisation modelling) would settle the tracer question: if such a model produces a structure comparable to the Giant Arc in size, membership, and significance at $z \sim 0.8$, then the paper's absence of gigaparsec structures in subhaloes would no longer count as evidence against $\Lambda$CDM.

Watch

Extended reading notes

Core claim

The central claim is that the full FLAMINGO-10K box, analysed at $z=0.7$ with subhalo masses $1$--$5 \times 10^{12}$ solar masses through Single-Linkage Hierarchical Clustering, Convex Hull of Member Spheres, and Minimal Spanning Tree algorithms, contains no gigaparsec-scale structures and only a few ultra-large structures with maximum pairwise separation above $370$ Mpc, and that the large-scale aspects of the simulation can be adequately represented by a Poisson point distribution. The paper further claims that a recent analysis concluding that gigaparsec patterns abound in a $\Lambda$CDM universe is flawed: it used a linkage scale of $95$ Mpc where $65$ Mpc is appropriate for exactly known simulated coordinates, it did not apply independent reality-assessment tests, and it drew a non sequitur from the absence of persistence among its own candidate structures. On this reanalysis, the Giant Arc and Big Ring are not reproduced, and the authors conclude that these structures present a more direct challenge to $\Lambda$CDM than previously claimed.

Load-bearing premise

The analysis assumes that FLAMINGO-10K subhaloes of mass $1$--$5 \times 10^{12}$ solar masses at $z=0.7$ trace the same large-scale structure as the MgII absorbers that define the Giant Arc; the paper itself notes that MgII gas cannot be modelled by dark matter particles or subhaloes, so if MgII gas is distributed more broadly, the absence of gigaparsec structures in the subhalo distribution would not demonstrate a $\Lambda$CDM challenge.

Editorial extensions

If this is right

No gigaparsec structure appears in any of the 100 random realisations of the full FLAMINGO-10K box, so the Giant Arc's ~1 Gpc extent is not reproduced in this $\Lambda$CDM simulation.
The large-scale subhalo distribution of FLAMINGO-10K is statistically indistinguishable from a Poisson point distribution, meaning the simulation lacks the coherent gigaparsec patterns claimed by the earlier analysis.
The earlier claim of abundant gigaparsec patterns is attributed to an inappropriately large linkage scale ($95$ Mpc) that favours chaining of unrelated clumps, rather than to genuine structure.
Because the Giant Arc and Big Ring lie in the same sky region and redshift slice, failing to reproduce even one of them - let alone the pair - supports the view that these are rare, cosmologically significant structures.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A direct extension would be to repeat the analysis using gas-phase MgII tracers from a full-physics hydrodynamical simulation; if those tracers reproduce gigaparsec structures, the paper's strongest conclusion would be weakened.
The near-Poisson large-scale distribution of FLAMINGO-10K subhaloes, if confirmed in other simulations, could indicate that $\Lambda$CDM lacks sufficient large-scale power, a possible hint of physics beyond the standard model.
Applying the same enhanced pipeline to other observed large-scale structures (for example, the Sloan Great Wall or the Quipu superstructure) would show whether the Giant Arc is a single outlier or part of a broader tension between observations and simulations.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The thing you should know: this paper is a serious, mostly fair methodological rebuttal to Sawala et al.'s claim that gigaparsec patterns abound in ΛCDM. Lopez and Clowes reanalyze the same FLAMINGO-10K subhalo data that Sawala used, but with a linkage scale appropriate for simulations (65 Mpc instead of 95 Mpc). Using the full box and 100 random subsets, they find that no candidate structure comes close to the Giant Arc in membership, significance, or maximum pairwise separation. That numerical result is credible and worth taking seriously.

What is new: the linkage-scale argument is well made. Sawala applied a scale calibrated for real MgII data, which has to accommodate redshift errors, peculiar velocities, and gaps in quasar coverage. Simulation data have none of those complications, so the mean-nearest-neighbour linkage of 65 Mpc is the right starting point. Using 95 Mpc on simulation points probably induces chaining, inflating the apparent abundance of gigaparsec structures. That is a genuine correction to the published analysis.

The paper also shows that the chosen subhalo distribution on these scales looks remarkably Poisson-like—an interesting and slightly worrying result for the simulation, even if the comparison is only visual.

Where it gets soft: the load-bearing assumption is that these subhaloes (mass 1–5×10^12 M_sun at z=0.7) trace the MgII absorbers that define the Giant Arc. The authors themselves note in Section 3.6 that MgII gas cannot be modeled by dark matter particles or subhaloes, citing Kauffmann et al. 2017, and they even suggest the HBT+ subhalo finder may under-represent structure. So the null result applies to this particular subhalo tracer, not necessarily to MgII absorbers. Without an independent tracer calibration, the conclusion that the GA presents a more direct challenge to ΛCDM is overreach. The paper would be stronger if it framed the result as a limitation of the subhalo-based test, or tested an alternative tracer.

Also minor: the Poisson equivalence is asserted from histogram overlap, not a formal statistical test; the linkage scale is fixed at 65 Mpc with no sensitivity run; and only one mass range is used. These are fixable and do not undermine the central numerical finding.

Overall, this paper deserves a serious referee. It is a legitimate correction to a high-profile claim, and the core statistical result seems solid. A referee should push hard on the tracer question and request sensitivity tests, but this is not a desk reject. It belongs in the conversation.

For anyone working on the Cosmological Principle or on using simulations to assess rare structures, this is a useful read. I would bring it to a reading group and would cite it in a paper that discusses FLAMINGO or the Giant Arc debate.

Referee Report

4 major / 6 minor

Summary. The paper reanalyzes the FLAMINGO-10K simulation data previously used by Sawala et al. (2025) to argue that gigaparsec-scale patterns are common in ΛCDM. The authors apply single-linkage hierarchical clustering (SLHC/FoF) with a linkage scale of 65 Mpc, together with CHMS and MST significance/overdensity estimators, to 100 random realizations of subhalo selections in a 2.8^3 Gpc^3 box at z=0.7, restricted to subhalo masses 1–5×10^12 M_sun and to candidate structures with N≥10. They report no gigaparsec structures, only a few structures exceeding a maximum pairwise separation of 370 Mpc, and they claim that the large-scale aspects of the FLAMINGO-10K subhalo distribution are adequately represented by random Poisson data. From this they conclude that the Giant Arc and Big Ring are more remarkable and present a more direct challenge to ΛCDM than Sawala et al. claimed. The paper also criticizes Sawala et al. for using an inappropriate linkage scale, for not applying independent significance tests, and for drawing a non-sequitur from structure persistence. A central admitted limitation is stated in Section 3.6: Mg II absorbers cannot currently be modeled by dark matter subhaloes, so the transfer of the null result to the observed Giant Arc is not established.

Significance. If the central claim is correct, the paper would substantially strengthen the case that the Giant Arc and Big Ring are rare or absent in at least one flagship ΛCDM simulation, directly contradicting the 'gigaparsec patterns abound' conclusion of Sawala et al. The paper is a useful methodological counterpoint: it demonstrates that the chosen linkage scale matters, applies two independent significance estimators (CHMS and MST), and compares against 100 random subhalo selections, which is a reasonable sample size for a null search. However, the significance is conditional on the assumption that the selected subhalo population traces Mg II absorbers on scales of hundreds of Mpc; the paper itself concedes in Section 3.6 that this assumption is unsupported, citing Kauffmann et al. (2017). In addition, the Poisson-equivalence claim is asserted from visual histogram similarity rather than quantified, and the single linkage scale and single mass range leave the robustness of the null result untested. The paper does not provide code or machine-checkable proofs; the analysis is described textually and through figures, which limits reproducibility but does not invalidate the results.

major comments (4)

[Section 3.6 and Section 4] The central inference—that the absence of gigaparsec structures in the FLAMINGO-10K subhalo distribution supports a more direct challenge to ΛCDM from the Giant Arc—requires that the selected subhaloes (masses 1–5×10^12 M_sun at z=0.7) trace the Mg II absorbers on scales of hundreds of Mpc. Section 3.6 explicitly states that Mg II cannot be modelled by dark matter particles or subhaloes, citing Kauffmann et al. (2017), and even suggests that the HBT+ subhalo catalogue may under-represent structure. The paper does not provide any calibration of the subhalo tracer against the observed clustering of Mg II absorbers on large scales. Without such a calibration, the reported null result describes only the subhalo distribution, not the existence or frequency of Giant Arc-like structures in ΛCDM. This limitation is load-bearing for the paper's conclusion and should either be resolved with an independent tracer calibration or the conclusion should be substantially softened.
[Section 4.1 and Figures 7–10] The claim that 'the large-scale aspects of the FLAMINGO-10K data could be adequately represented by a Poisson point distribution' is based on visual inspection of histograms and scatter plots ('closely aligned', 'extremely similar profiles') rather than on a quantitative test. No Kolmogorov–Smirnov, Anderson–Darling, or other two-sample test statistic is reported for the distributions of significance, overdensity, membership, or maximum pairwise separation. Moreover, the random Poisson data are generated by replacing the subhalo coordinates with random positions while matching the field density; the random thinning to the very low Mg II-like density suppresses clustering, so a similarity to Poisson is expected and does not by itself demonstrate that the simulation lacks physical structure. The authors should provide a quantitative comparison and discuss the effect of random thinning on the clustering measures.
[Section 4 and Section 2.1] The analysis uses a single linkage scale of 65 Mpc, a single subhalo mass range (1–5×10^12 M_sun), and a single membership threshold N≥10. The paper criticizes Sawala et al. for using a larger linkage scale, but it does not test whether the conclusion 'no gigaparsec structures' is robust to reasonable variations in the linkage scale (e.g., 55–75 Mpc), to different mass cuts, or to different membership thresholds. Given that the Giant Arc itself was identified with a linkage scale of 95 Mpc in Mg II data, and that the appropriate mapping between linkage scales for different tracers is model-dependent, a sensitivity analysis is needed to support the strong 'nowhere to be seen' claim. Without it, the null result is conditional on the authors' chosen parameters.
[Sections 3.1, 3.4, and 5] The comparisons of simulated candidate structures with the Giant Arc use benchmark values (membership, significance, maximum pairwise separation) taken from the authors' own earlier analyses of the GA and BR, yet Section 5 states that 'the SLHC algorithm, or other MST-type tests, are not strictly applicable or appropriate to the Mg II data' because of intrinsic spatial variations. This creates a tension: the paper uses those same methods to define the GA significance threshold that the simulation results are measured against, while simultaneously arguing that the methods are not strictly appropriate for the real data. The authors should clarify how the GA significance values should be interpreted given this caveat, or provide an independent, simulation-calibrated measure of the rarity of the observed structures.

minor comments (6)

[Figures 3–10 captions] The captions repeatedly state '100 cubes (28003 Mpc3)' and 'the100 cubes'; these should read '100 cubes (2800^3 Mpc^3)' and 'the 100 cubes' with proper superscript formatting and spacing.
[Abstract and Section 1] The abstract contains 'full2.83 Gpc3' without spaces and with a poorly rendered superscript; this should be '2.8^3 Gpc^3' (or '2.83 Gpc^3' with a clear superscript) for readability.
[Figure 2] Figure 2 is not cited anywhere in the text; the authors should either refer to it explicitly where the SDSS footprint is discussed (e.g., in Section 3.6) or remove it to avoid an uncited figure.
[Section 4.1] The Poisson comparison uses 100 cubes for the FLAMINGO-10K data but only 40 cubes for the random Poisson data; the authors should justify why 40 realizations are sufficient or use the same number for both.
[Section 2.1] The derivation of the 95 Mpc linkage scale for the Mg II data depends on the specific choice of a 1.5σ underdense patch in the probe distribution and on adding peculiar-velocity errors in quadrature; the sensitivity of the final scale to these choices should be discussed, since this is the basis for criticizing Sawala et al.
[Affiliation and title] The affiliation 'University of Lancashire (formerly, Central Lancashire)' appears inconsistent with the title page; please verify the correct institutional name.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the FLAMINGO-10K statistics are computed with a linkage scale derived from field density, and the GA comparison values are external observational measurements, not fitted parameters.

full rationale

The paper's derivation chain is not circular. The central FLAMINGO-10K analysis uses a linkage scale of 65 Mpc obtained from the Poisson mean-nearest-neighbour relation rbar ≈ 0.55(1/rho)^{1/3} evaluated at the field density of the subhalo sample; no parameter is fitted to reproduce the Giant Arc. The comparison thresholds (GA-main membership 44, GA-all membership 55, maximum pairwise separations 742/886 Mpc, MST/CHMS significances -4.7/-4.5 sigma) are quoted from the authors' earlier observational analyses of Mg II absorbers, i.e., external measurements rather than outputs of the present simulation fit. Although the paper cites the authors' own prior work for the GA and BR, those citations carry independent observational content and are not used as a uniqueness theorem or to forbid alternatives. Section 3.6 (Representing Mg II gas with simple CDM particles and subhaloes) explicitly concedes that Mg II gas cannot be modelled by dark-matter subhaloes, citing Kauffmann et al. (2017); this is a tracer-mismatch limitation that affects the external validity of the null result, but it does not make the internal statistics circular. Similarly, the Poisson comparison is an empirical statement about the thinned subhalo sample; objections about thinning suppressing clustering are methodological, not circularity. No equation in the paper reduces to an input by construction, and no prediction is statistically forced by a fitted parameter renamed as an output.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The analysis depends on hand-chosen thresholds (linkage scale, membership cutoff, number of realizations) and on the assumption, which the paper itself questions, that subhaloes trace Mg II absorbers. No new physical entities are introduced.

free parameters (3)

Linkage scale = 65 Mpc
Derived from the Poisson mean nearest-neighbour separation for the MgII field density; the central result depends on this choice, and the paper argues the 95 Mpc scale used by Sawala et al. is inappropriate for simulations.
Membership cutoff N_min = 10
Applied to define candidate structures in all analyses; changes the histograms and the number of identified uLSSs.
Number of random realizations = 100 (FLAMINGO), 40 (Poisson)
The claim that no gigaparsec structures exist in FLAMINGO-10K is limited by the 100 random subset selections; the Poisson comparison uses only 40 cubes.

assumptions (5)

domain assumption The mean nearest-neighbour formula r≈0.55(1/ρ)^{1/3} for a Poisson distribution is applicable to the FLAMINGO-10K subhalo sample.
Used in Section 2.1 to set the 65 Mpc linkage scale; the subhalo distribution is clustered, so the appropriate linkage scale may differ.
domain assumption Subhaloes in the mass range 1-5×10^12 M_sun at z=0.7 are adequate tracers of Mg II absorbers for large-scale structure comparison.
Section 3.6 cites Kauffmann et al. suggesting Mg II cannot be modelled by subhaloes, yet the analysis relies on this mapping to compare with the Giant Arc.
domain assumption The significance values of the Giant Arc (MST -4.7σ, CHMS -4.5σ) from the authors' earlier papers are valid benchmarks.
Used as thresholds in Figures 3-6; these were computed with methods the paper itself acknowledges are imperfect for Mg II data.
domain assumption The FLAMINGO-10K output at z=0.7 represents the relevant regime for the Giant Arc at z≈0.8.
Section 1 states the coordinates 'essentially correspond' but does not model the difference in structure growth between these redshifts.
standard math A Poisson point process is a valid null model for large-scale structure at the sampled density.
Used in Section 4.1 as the backdrop for comparison; it assumes no clustering on large scales in the null.

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Cite this review

Pith. "Pith review of Gigaparsec structures are nowhere to be seen in $\Lambda$CDM: an enhanced analysis of LSS in FLAMINGO-10K simulations." pith.science (2026). https://pith.science/paper/XLJLMUHN

@misc{pith2026250414940,
  author       = {Pith},
  title        = {Pith review of: Gigaparsec structures are nowhere to be seen in $\Lambda$CDM: an enhanced analysis of LSS in FLAMINGO-10K simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XLJLMUHN}},
  note         = {Machine review of arXiv:2504.14940}
}

abstract

Recently, Sawala et al. 2025 claimed to refute the cosmological significance of the Giant Arc based on their analysis of the FLAMINGO-10K simulation data. In our paper here, we highlight several shortcomings of the authors' analysis. We then perform an enhanced analysis on the FLAMINGO-10K simulation data with applications of: the Single-Linkage Hierarchical Clustering (SLHC), the Convex Hull of Member Spheres (CHMS), and the Minimal Spanning Tree (MST) algorithms. Using the full $2.8^3$ Gpc$^3$ FLAMINGO-10K box, with subhaloes at $z=0.7$, and $100$ random realisations (from random subset selections) we find no gigaparsec structures in FLAMINGO-10K, and only a few ultra-large large-scale structures (uLSSs, structures exceeding a maximum pairwise separation of $370$ Mpc). Somewhat surprisingly, we found that the large-scale aspects of the FLAMINGO-10K data could be adequately represented by a Poisson point distribution. The enhanced analysis presented here further supports the remarkable nature of the Giant Arc as a cosmologically-significant structure. Of course, the Giant Arc is also accompanied by a second uLSS, the Big Ring. The analysis presented here builds on the work presented by Sawala et al., but amends the application of their statistical assessments. We do not yet know why there appears to be such a large discrepancy between the FLAMINGO-10K data and the observed LSS in MgII absorbers. Perhaps the results presented here might suggest that the GA, and especially the GA + BR, presents a more direct challenge to $\Lambda$CDM. In contrast to the conclusion of Sawala et al. that `gigaparsec patterns abound in a $\Lambda$CDM universe' we find that they are nowhere to be seen.

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Forward citations

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Reference graph

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

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T. Sawala, M. Teeriaho, C.S Frenk, J. Helly, A. Jenkins, G. Racz, M. Schaller and J. Schaye, The Emperor’s New Arc: gigaparsec patterns abound in aΛCDM universe, Mon. Not. Roy. Astron. Soc.(2025) [arXiv:2502.03515]

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