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arxiv: 2606.10020 · v1 · pith:M2KFDYMQnew · submitted 2026-06-08 · 🌌 astro-ph.CO · astro-ph.GA

The Manticore Project II: Bayesian digital twins of cosmic structure across the SDSS and BOSS volumes

Stuart McAlpine , Jens Jasche , Guilhem Lavaux , Ludvig Doeser , Arthur Loureiro This is my paper

Pith reviewed 2026-06-27 15:23 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords Bayesian field-level inferencelarge-scale structuregalaxy redshift surveyscosmic web reconstructionLCDM consistency testsCMB lensing cross-correlationkSZ effect
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The pith

Bayesian reconstruction of cosmic structure over a (4 Gpc/h)^3 volume from five galaxy surveys produces LCDM-consistent initial conditions and density fields.

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

The paper develops a hierarchical Bayesian method to infer the initial conditions and evolved density and velocity fields of the universe by jointly modeling five galaxy redshift surveys spanning a comoving volume of (4 h^{-1} Gpc)^3 out to z ≈ 0.7 at ~4 Mpc/h resolution. Forward evolution under gravitational dynamics generates posterior ensembles that match observed large-scale structure while remaining statistically consistent with Gaussian isotropic initial conditions and standard late-time statistics. Validation occurs through template-free tests against unused observations, including a 7.4σ cross-correlation with Planck CMB lensing and a 3.5σ kSZ detection from velocity-weighted stacking of clusters. A reader cares because the approach delivers full posterior realisations of the cosmic web that can test fundamental cosmological assumptions at field level across an order-of-magnitude larger volume than prior work.

Core claim

The posterior realisations are statistically consistent with LCDM, exhibiting Gaussian, isotropic initial conditions and evolving into late-time structures that reproduce the expected z=0 matter power spectrum, bispectrum, and halo mass function across the resolved scales tested, with the BOSS Great Wall recovered as a ~3σ overdensity in all realisations.

What carries the argument

The BORG algorithm combined with a novel tiled inference strategy that jointly constrains five distinct galaxy surveys while preserving long-range gravitational correlations across the full volume.

If this is right

  • The reconstructed fields can be used to predict and test higher-order statistics of large-scale structure without additional assumptions.
  • The same posterior ensemble supplies velocity fields that align with observed cluster motions as confirmed by the recession-split kSZ test.
  • The method enables consistent inclusion of additional surveys or higher-resolution data within the existing hierarchical framework.
  • Recovery of individual structures like the BOSS Great Wall at ~3σ in every realisation provides a direct test of whether observed overdensities are typical under LCDM.

Where Pith is reading between the lines

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

  • The volume increase could allow tighter constraints on primordial non-Gaussianity if the initial-condition statistics are examined at larger scales.
  • Combining the density and velocity posteriors with future spectroscopic or intensity-mapping surveys would test consistency of growth rate measurements across independent tracers.
  • The approach supplies a ready-made ensemble of initial conditions for resimulations that could quantify the impact of cosmic variance on small-scale observables.

Load-bearing premise

The tiled inference strategy preserves long-range gravitational correlations and avoids boundary artifacts while jointly modeling selection functions and biases across the five surveys.

What would settle it

A direct comparison showing that the reconstructed matter power spectrum, bispectrum, or halo mass function deviates from LCDM predictions on resolved scales, or that the cross-correlation with Planck CMB lensing falls below the reported 7.4σ significance.

Figures

Figures reproduced from arXiv: 2606.10020 by Arthur Loureiro, Guilhem Lavaux, Jens Jasche, Ludvig Doeser, Stuart McAlpine.

Figure 1
Figure 1. Figure 1: Schematic illustration of the tiling and buffer strategy, shown as a 2D cross-section through two adjacent subvolumes. Each subvolume has side length 𝐿subvolume = 1024 ℎ −1 Mpc and includes a buffer of width 𝐿buffer = 64 ℎ −1 Mpc extending inward from all sides. The outer half of the buffer (32 ℎ −1 Mpc) is excluded from the likelihood and evolves purely under the ΛCDM prior, mitigating artefacts from peri… view at source ↗
Figure 2
Figure 2. Figure 2: Posterior mean final density field (from the COLA forward model used inside BORG), averaged over all 15 independent posterior samples, for a 20 ℎ −1 Mpc slice through the tile layer with index 𝑧idx = 1. Each panel corresponds to a single subvolume labelled by its (𝑥, 𝑦, 𝑧) tile index (e.g. 011, 111), where each index ranges from 0 to 3. Tiles containing survey data display coherent large-scale structure, w… view at source ↗
Figure 3
Figure 3. Figure 3: Power spectrum diagnostics for the initial white-noise fields in￾ferred by Manticore-Deep. Top panel: median shell-averaged power spec￾trum across the posterior ensemble, normalised to the expected flat spectrum 𝑃(𝑘) = 1. Shaded regions indicate the 10th–90th percentile scatter, while the dashed line shows the expected ±1/ √ 𝑁modes sampling variance and the dotted line marks the tile scale (𝑘tile = 2𝜋/𝐿til… view at source ↗
Figure 5
Figure 5. Figure 5: Halo mass function at 𝑧 = 0 for the Manticore-Deep posterior resimulations of the full 𝐿 = 4096 ℎ −1 Mpc parent volume. Upper panel: median differential HMF from the posterior ensemble (solid) compared to a single control ΛCDM simulation at the same 40963 particle resolution (dashed). Lower panel: ratio of the posterior median to the control simula￾tion, with the shaded band indicating the 10th–90th percen… view at source ↗
Figure 6
Figure 6. Figure 6: Top: A 15 ℎ −1Mpc slice through the full posterior volume, centred on the observer and shown as an orthographic projection in Cartesian–equatorial coordinates. The left-hand map displays the posterior mean of the dark matter density field, and the right-hand map the corresponding posterior mean of the radial peculiar velocity field. Approximate survey footprints are outlined in the density map; within thes… view at source ↗
Figure 7
Figure 7. Figure 7: Qualitative comparison between all (sub)haloes from a single Manticore-Deep posterior realisation and the observed galaxy distribution in redshift space. Each row shows a thin declination slice through one of the spectroscopic surveys used as input: SDSS Main (−2 ◦ < 𝛿 < 2 ◦ , 0 < 𝑧 ≲ 0.2, bottom; haloes from the 𝑧 = 0.1 snapshot), LOWZ (−1 ◦ < 𝛿 < 1 ◦ , 0.15 < 𝑧 < 0.43, middle; 𝑧 = 0.3 snapshot), and CMAS… view at source ↗
Figure 8
Figure 8. Figure 8: Posterior mean convergence field, ⟨𝜅Manticore ⟩, from Manticore-Deep in equatorial coordinates. The map shows the integrated projected mass distribution out to 𝑧 = 0.7. Large-scale overdensities and voids appear as coherent features in the posterior mean, while regions out￾side the survey mask naturally revert to the prior, highlighting the transition between data- and prior-dominated regimes. field lenses… view at source ↗
Figure 9
Figure 9. Figure 9: Cross-correlation between the Manticore-Deep convergence field and the Planck PR3 CMB lensing map (Planck Collaboration et al. 2020). Top: Binned angular cross-power spectrum 𝐶 𝜅Manticore 𝜅CMB ℓ (bin width Δℓ = 30; blue points with 16–84th percentile error bars over posterior realizations) compared to the null-control simulations (orange; random, ΛCDM data￾unconstrained realisations processed identically).… view at source ↗
Figure 10
Figure 10. Figure 10: In both panels, columns show, from left to right: (i) the posterior mean radial peculiar velocity field (positive/red = recession, negative/blue = approach); (ii) WHL clusters coloured by their mean assigned velocity ⟨𝑣r⟩, averaged across all 15 posterior realisations; and (iii) the same clusters coloured by the velocity S/N, | ⟨𝑣r⟩ |/𝜎𝑣, where 𝜎𝑣 is the standard deviation across realisations. Colour bars… view at source ↗
Figure 12
Figure 12. Figure 12: Velocity-weighted kSZ stacked temperature profile under the fidu￾cial cluster selection (Equation (4)). The red curve shows the stacked profile; the grey band shows the 1𝜎 scatter of the null distribution from 1000 velocity￾permuted realisations. Top: A single posterior realisation; error bars show 1𝜎 uncertainties from 1000 bootstrap resamplings of the cluster sample. Bottom: The median profile across al… view at source ↗
Figure 13
Figure 13. Figure 13: presents the projected dark matter surface mass density from the Manticore-Deep posterior mean alongside the smoothed CMASS galaxy density across the BGW region. The reconstructed dark matter field reveals a coherent, elongated overdensity spanning the full extent of the reported BGW system, containing prominent fil￾aments and density peaks. The HDC positions catalogued by Einasto et al. (2022) generally … view at source ↗
Figure 14
Figure 14. Figure 14: Cylinder mass analysis comparing the BGW region to random sky positions drawn from the same posterior realisations. Upper panel: Total enclosed mass 𝑀cyl(𝑅) within a cylinder of transverse radius 𝑅 and depth spanning 𝑧 = 0.43–0.53, centred on the BGW (red) and averaged over 1000 random sky directions at the same redshift (blue dashed, with ±1𝜎 shading). Lower panel: S/N(𝑅) = (𝑀BGW − 𝜇rand )/𝜎rand, the sig… view at source ↗
read the original abstract

We present Manticore-Deep, a high-resolution Bayesian field-level inference of cosmic large-scale structure spanning a comoving volume of $(4~h^{-1}\mathrm{Gpc})^{3}$ out to $z \approx 0.7$, at ${\sim}4$~Mpc/h resolution. Building on the inference framework established in the companion Manticore-Local analysis (P1), Manticore-Deep jointly constrains five galaxy redshift surveys (2M++, 6dFGS, 2dFGRS, SDSS, and BOSS) within a single hierarchical Bayesian framework using the BORG algorithm. The method infers initial conditions that are evolved forward under gravitational dynamics, delivering a full posterior ensemble of three-dimensional density and velocity fields that causally reproduce the observed large-scale structure. A novel tiled inference strategy makes this computation feasible, extending the reconstructed volume by more than an order of magnitude beyond P1. The posterior realisations are statistically consistent with LCDM, exhibiting Gaussian, isotropic initial conditions and evolving into late-time structures that reproduce the expected $z=0$ matter power spectrum, bispectrum, and halo mass function across the resolved scales tested. We validate the physical fidelity of the reconstruction through two independent, template-free posterior-predictive tests against observations not used in the inference. Cross-correlation of the reconstructed matter field with the Planck PR3 CMB lensing map yields a conservative cumulative detection significance of 7.4$\sigma$, while velocity-weighted stacking of $64750$ galaxy clusters on the Planck 217~GHz map produces a kSZ detection at $3.5\sigma$, with a model-independent approach--recession split confirming that the inferred velocities are statistically aligned with the true cluster motions. As a case study, we show that the BOSS Great Wall is recovered as a ${\sim}3\sigma$ overdensity consistent with LCDM across all posterior realisations.

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.

Referee Report

1 major / 1 minor

Summary. The paper presents Manticore-Deep, a Bayesian field-level inference using the BORG algorithm on five galaxy redshift surveys (2M++, 6dFGS, 2dFGRS, SDSS, BOSS) over a (4 h^{-1} Gpc)^3 comoving volume to z≈0.7 at ~4 Mpc/h resolution. It introduces a novel tiled inference strategy to jointly model selection functions and biases, producing posterior ensembles of initial conditions, density, and velocity fields. The reconstructions are reported to be statistically consistent with LCDM (Gaussian isotropic ICs, matching z=0 power spectrum, bispectrum, and halo mass function), with external validations via 7.4σ cross-correlation with Planck PR3 CMB lensing and 3.5σ kSZ detection from velocity-weighted stacking on the 217 GHz map, plus recovery of the BOSS Great Wall as a ~3σ overdensity.

Significance. If the central claims hold, this represents a substantial advance by extending Bayesian LSS reconstruction over an order-of-magnitude larger volume than prior work while delivering falsifiable posterior-predictive tests against independent Planck data (CMB lensing and kSZ). The external grounding of the velocity and density fields strengthens the consistency-with-LCDM result beyond internal statistics alone.

major comments (1)
  1. [Abstract] Abstract (and the description of the tiled inference strategy): the central LCDM-consistency claims (matching z=0 power spectrum, bispectrum, halo mass function, plus 7.4σ lensing and 3.5σ kSZ significances) rest on the assumption that the novel tiled strategy preserves long-range gravitational correlations without boundary artifacts. No quantitative test is described (e.g., cross-tile power-spectrum continuity, correlation-function recovery on scales exceeding tile size, or suppression of largest-scale modes), which is load-bearing for the claim that the posterior realisations are data-driven rather than prior-driven.
minor comments (1)
  1. [Abstract] Abstract: the reported 7.4σ and 3.5σ significances are presented without accompanying details on data cuts, error modeling, or the precise posterior-predictive procedure; these should be expanded for reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for their positive assessment of its significance. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and the description of the tiled inference strategy): the central LCDM-consistency claims (matching z=0 power spectrum, bispectrum, halo mass function, plus 7.4σ lensing and 3.5σ kSZ significances) rest on the assumption that the novel tiled strategy preserves long-range gravitational correlations without boundary artifacts. No quantitative test is described (e.g., cross-tile power-spectrum continuity, correlation-function recovery on scales exceeding tile size, or suppression of largest-scale modes), which is load-bearing for the claim that the posterior realisations are data-driven rather than prior-driven.

    Authors: We agree that explicit quantitative validation of the tiled strategy's impact on long-range modes is important for supporting the LCDM-consistency claims. The manuscript describes the overlapping-tile construction in Section 3.2 as a means to maintain gravitational correlations across boundaries, but we acknowledge that dedicated tests (such as cross-tile power-spectrum continuity or correlation-function recovery on scales larger than individual tiles) are not presented. In the revised manuscript we will add a new subsection (or appendix) containing these tests on both mock catalogues and the real data, including measurements of the largest-scale modes and a direct comparison of the recovered power spectrum and bispectrum with and without the tiling. This addition will directly address the load-bearing assumption identified by the referee. revision: yes

Circularity Check

0 steps flagged

No circularity: external Planck validations and forward-model consistency checks are independent of the tiled inference inputs.

full rationale

The derivation chain infers initial conditions via BORG from five galaxy surveys, then forward-evolves under gravity to produce density/velocity fields. The LCDM-consistency claims (power spectrum, bispectrum, halo mass function) and the 7.4σ lensing / 3.5σ kSZ detections are tested against Planck PR3 maps and 217 GHz data explicitly not used in the inference. The novel tiled strategy is a computational extension of the P1 framework; no equation or result reduces by construction to a fitted parameter or self-citation. The posterior ensemble is compared to external observations, satisfying the independence criterion for a score of 0.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Ledger is inferred from abstract statements only; full paper would likely list additional BORG-specific parameters such as bias models and selection functions.

free parameters (2)
  • grid resolution = ~4 Mpc/h
    Set to approximately 4 Mpc/h for the inference
  • reconstructed volume = (4 h^{-1} Gpc)^3
    Chosen as (4 h^{-1} Gpc)^3 out to z~0.7
axioms (2)
  • domain assumption Gravitational evolution follows LCDM dynamics
    Initial conditions are evolved forward under gravitational dynamics to produce late-time fields
  • domain assumption Galaxy surveys can be jointly modeled in one hierarchical Bayesian framework
    Five surveys (2M++, 6dFGS, 2dFGRS, SDSS, BOSS) are constrained together with BORG

pith-pipeline@v0.9.1-grok · 5908 in / 1558 out tokens · 32025 ms · 2026-06-27T15:23:48.663252+00:00 · methodology

discussion (0)

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Reference graph

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