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arxiv: 2605.23367 · v1 · pith:US35ZQ6Nnew · submitted 2026-05-22 · 🌌 astro-ph.CO

Cosmological constraints from neighbor-density-weighted marked correlation functions

Xu Xiao , Xiao-Dong Li , Yiqi Huang , Le Zhang This is my paper

Pith reviewed 2026-05-25 03:23 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords marked correlation functionscosmological constraintstwo-point correlation functiongalaxy clusteringdark energyneutrino massGaussian process emulatorsfigure of merit
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The pith

Neighbor-density-weighted marked correlation functions improve cosmological constraints by factors of 1.7-2.5 over the standard two-point correlation function.

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

The paper examines whether weighting galaxy pairs by local neighbor density in marked correlation functions can recover additional cosmological information that the ordinary redshift-space two-point correlation function misses. The authors train Gaussian-process emulators on 129 simulations spanning a w0waCDM plus neutrino-mass model, then measure how much the figure of merit in the Omega_m-sigma_8 plane rises when several mark strengths are combined. Gains reach 1.7-2.5 for three-mark sets and remain similar for five-mark sets, with density and gradient marks adding extra power only in the angular statistic. A reader would care because next-generation surveys will map billions of galaxies, so any reliable way to squeeze more parameters from the same data directly sharpens tests of dark energy and neutrino mass. The marked statistics also prove stable when the fitting scale or galaxy sample is altered.

Core claim

Using the Kun suite of 129 w0waCDM+sum m_nu simulations in 1 h^-1 Gpc boxes, the work builds emulators for the normalized scale statistic W^alpha(s) and the angular statistic W^alpha_Delta s(mu), then demonstrates that joint analyses with multiple mark parameters alpha raise the FoM in the Omega_m-sigma_8 plane by factors of 1.7-2.5 relative to the unmarked 2PCF, while density and normalized-gradient marks are nearly redundant for isotropic statistics but complementary for angular statistics, improving the FoM by up to 43 percent.

What carries the argument

Neighbor-density-weighted marked correlation functions (MCFs) with variable mark parameter alpha, emulated by Gaussian processes on the Kun-suite simulations.

If this is right

  • Three-mark combinations raise the FoM by 1.7-2.5 depending on the statistic and mark definition.
  • Five-mark combinations produce comparable gains of 1.9-2.4.
  • Density and normalized-gradient marks are nearly redundant for isotropic statistics but complementary for angular statistics, adding up to 43 percent extra FoM.
  • The marked statistics remain robust when the analysis scale range or halo selection is changed.
  • The angular statistic retains extra cosmological information that is less sensitive to tracer selection.

Where Pith is reading between the lines

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

  • Applying the same multi-mark analysis to real catalogs from DESI or Euclid could tighten neutrino-mass bounds without requiring larger survey volumes.
  • The observed complementarity between mark types suggests that a joint density-plus-gradient mark might yield still larger gains in full three-dimensional analyses.
  • If the emulator accuracy holds when the simulation volume is increased, the method should scale directly to the data volumes expected from next-generation surveys.
  • Comparing the marked statistics against alternative higher-order probes such as three-point functions on the same simulations would clarify whether the gains are unique or overlapping.

Load-bearing premise

The Gaussian-process emulators trained on the 129 simulations accurately reproduce the marked statistics across the full parameter space with negligible interpolation error.

What would settle it

Repeating the full FoM comparison on an independent simulation suite or on mock catalogs that include realistic observational systematics would falsify the claimed improvement if the gain shrinks below 1.2.

Figures

Figures reproduced from arXiv: 2605.23367 by Le Zhang, Xiao-Dong Li, Xu Xiao, Yiqi Huang.

Figure 1
Figure 1. Figure 1: FIG. 1: Sampling of the 129 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Environmental quantities in a [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Scale-dependent marked statistic [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Angular marked statistic [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Leave-one-out validation errors of the GPR emulator. The left panel shows the 68th-percentile fractional error for the scale-dependent [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Covariance matrices for [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: , this case exhibits stronger parameter degeneracies, resulting in biased posteriors where the 1𝜎 contours do not fully recover the true cosmology. Taken together, these results show that the primary gain from MCFs arises from combining multiple environmental weight￾ings, which effectively reduces both parameter uncertainties and degeneracies, leading to a substantially smaller allowed parameter volume. 𝑊b… view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: 1D posteriors for [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: The MCMC results for [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Similar to Figure [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Same configurations as in Figure [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Same configurations as in Figure [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Similar to Figure [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
read the original abstract

We investigate whether neighbor-density-weighted marked correlation functions (MCFs) can extract cosmological information beyond the standard redshift-space two-point correlation function (2PCF). Using the Kun suite of 129 $w_0w_a$CDM$+\sum m_\nu$ simulations in $1~h^{-1}{\rm Gpc}$ boxes, we construct Gaussian-process emulators for the normalized scale statistic $\widehat{W}^{\alpha}(s)$ and the angular statistic $\widehat{W}^{\alpha}_{\Delta s}(\mu)$. We perform joint analyses combining multiple mark parameters $\alpha$ and quantify the information gain using the FoM in the $\Omega_m$--$\sigma_8$ plane. Relative to the 2PCF case, three-mark combinations improve the FoM by factors of $1.7$--$2.5$, while five-mark combinations increase the gain to $1.9$--$2.4$, depending on the statistic and mark definition. We further compare density and normalized-gradient marks, finding that they are nearly redundant for isotropic statistics but complementary for angular statistics, where their combination improves the FoM by up to $43\%$. Tests of scale range and halo selection show that the marked statistics remain robust under changes in analysis choices, with the angular statistic retaining additional cosmological information that is less sensitive to tracer selection. Our results demonstrate that MCFs substantially enhance cosmological constraints beyond the standard 2PCF and provide a robust probe for next-generation galaxy surveys.

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

2 major / 2 minor

Summary. The manuscript investigates whether neighbor-density-weighted marked correlation functions (MCFs) extract additional cosmological information beyond the redshift-space 2PCF. Using the Kun suite of 129 w0waCDM+∑mν simulations, the authors train Gaussian-process emulators for the normalized scale statistic Ŵ^α(s) and angular statistic Ŵ^α_Δs(μ), then quantify information gain via FoM in the Ωm–σ8 plane for multi-mark combinations (three-mark: 1.7–2.5× improvement; five-mark: 1.9–2.4×). They also compare density vs. normalized-gradient marks and test robustness to scale range and halo selection.

Significance. If the emulator-based results hold, the work would be significant for next-generation surveys by showing that MCFs can deliver substantial FoM gains over the 2PCF with modest additional computational cost. The use of independent N-body simulations rather than parameter-fitting circularity is a methodological strength, and the reported complementarity between mark types for angular statistics is a concrete, testable finding.

major comments (2)
  1. [Abstract / emulator section] Abstract and emulator construction section: the headline FoM gains (1.7–2.5× for three-mark combinations) rest on the assumption that the GP emulators for Ŵ^α(s) and Ŵ^α_Δs(μ) reproduce the true dependence on the full ≥6-dimensional parameter vector (Ωm, σ8, w0, wa, ∑mν, plus h, ns) with negligible interpolation error. Only 129 training points are used for statistics that weight small-scale neighbor densities and are therefore more nonlinear than the plain 2PCF; no cross-validation, held-out error, or covariance-inflation metrics are reported. This directly undermines the quantitative central claim.
  2. [Results / joint analyses] Results section on joint analyses: the claim that five-mark combinations increase the gain to 1.9–2.4× and that density + gradient marks improve angular FoM by up to 43% is presented without any demonstration that the emulator error budget has been propagated into the reported contours or FoM values. If emulator variance is comparable to the reported gains, the improvements could be artifacts of sparse sampling in parameter space.
minor comments (2)
  1. [Methods] The precise definition of the normalized statistics Ŵ^α(s) and Ŵ^α_Δs(μ) (including how the mark weighting is applied and normalized) should be stated explicitly in the main text rather than deferred entirely to appendices.
  2. [Figures] Figure captions for the FoM comparison plots should include the exact mark parameter values α used in each combination and the covariance estimation method.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and for highlighting the importance of emulator validation to support the quantitative claims. We address each major comment below and will revise the manuscript to incorporate the requested checks.

read point-by-point responses

  1. Referee: [Abstract / emulator section] Abstract and emulator construction section: the headline FoM gains (1.7–2.5× for three-mark combinations) rest on the assumption that the GP emulators for Ŵ^α(s) and Ŵ^α_Δs(μ) reproduce the true dependence on the full ≥6-dimensional parameter vector (Ωm, σ8, w0, wa, ∑mν, plus h, ns) with negligible interpolation error. Only 129 training points are used for statistics that weight small-scale neighbor densities and are therefore more nonlinear than the plain 2PCF; no cross-validation, held-out error, or covariance-inflation metrics are reported. This directly undermines the quantitative central claim.

    Authors: We agree that the absence of reported cross-validation or held-out error metrics leaves the emulator accuracy unquantified and weakens the central claims. The original manuscript describes the GP construction but does not include these diagnostics. In the revision we will add a new subsection presenting leave-one-out cross-validation results, mean absolute percentage errors on held-out simulations, and an assessment of whether interpolation errors remain subdominant to the covariance used in the FoM calculation. revision: yes

  2. Referee: [Results / joint analyses] Results section on joint analyses: the claim that five-mark combinations increase the gain to 1.9–2.4× and that density + gradient marks improve angular FoM by up to 43% is presented without any demonstration that the emulator error budget has been propagated into the reported contours or FoM values. If emulator variance is comparable to the reported gains, the improvements could be artifacts of sparse sampling in parameter space.

    Authors: We acknowledge that emulator uncertainties were not propagated into the reported FoM values or contours. In the revised manuscript we will add explicit tests that either (i) inflate the data covariance by the measured emulator variance or (ii) recompute the FoM after adding a diagonal emulator-error term, and we will report the resulting changes to the quoted improvement factors. This will either confirm the robustness of the gains or qualify them appropriately. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation relies on external simulations and standard emulation

full rationale

The paper measures marked correlation functions directly on the independent Kun suite of 129 N-body simulations, trains Gaussian-process emulators on those measurements, and then compares FoM values between the 2PCF and various MCF combinations. No step equates a reported prediction or constraint to a fitted input by construction, invokes a self-citation as the sole justification for a uniqueness claim, or renames an input quantity as an output. The emulator step is a standard interpolation whose accuracy is an external assumption rather than a definitional identity, and the FoM gains are computed from the same simulation measurements for all statistics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the fidelity of the Gaussian-process emulators and on the assumption that the 129 simulations adequately sample the relevant cosmological parameter space; no new physical entities are introduced.

axioms (1)
  • domain assumption Standard flat w0waCDM cosmology with massive neutrinos governs the simulated large-scale structure.
    Invoked implicitly by the choice of simulation suite and parameter space.

pith-pipeline@v0.9.0 · 5800 in / 1262 out tokens · 46780 ms · 2026-05-25T03:23:49.423624+00:00 · methodology

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Reference graph

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