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arxiv: 2504.20478 · v5 · submitted 2025-04-29 · 🌌 astro-ph.CO

Tomographic Alcock-Paczynski Test with Marked Correlation Functions

Liang Xiao , Limin Lai , Zhujun Jiang , Xiao-Dong Li , Le Zhang This is my paper

Pith reviewed 2026-05-22 18:53 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords Alcock-Paczynski testmarked correlation functionstomographic analysisdark energy equation of stateprincipal component analysisredshift-space distortionscosmological constraintsfuture spectroscopic surveys
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The pith

Marked correlation functions with multiple density weights improve tomographic Alcock-Paczynski constraints on matter density and dark energy equation of state by 48 and 45 percent.

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

The paper demonstrates that marked correlation functions, which assign weights based on local galaxy density, extract more information from the tomographic Alcock-Paczynski test than the standard two-point correlation function. This test uses the redshift evolution of apparent shapes and sizes to isolate the expansion history from redshift-space distortions. Multiple density weights reduce uncertainties on the matter density parameter Omega_m by 48 percent and on the dark energy equation of state w by 45 percent in flat wCDM models. A new principal component analysis compression projects the high-dimensional measurements into a small set of eigenmodes that retain most of the cosmological signal and outperform simple bin averaging by an extra 40 percent in precision. The framework stays effective even after realistic redshift errors are added, supporting its use in upcoming spectroscopic surveys.

Core claim

Integrating marked correlation functions into the tomographic Alcock-Paczynski test shows that multiple density weights outperform the traditional two-point correlation function, cutting uncertainties on Omega_m by 48 percent and on w by 45 percent. The introduced PCA compression scheme projects high-dimensional statistical measurements into compact eigenmodes while preserving most cosmological information, delivering an additional roughly 40 percent reduction in error margins compared with lossy coarse binning. The combined approach remains robust when realistic redshift errors from future surveys are included and continues to produce tight constraints.

What carries the argument

Marked correlation functions using multiple density weights together with principal component analysis compression inside tomographic Alcock-Paczynski tests.

If this is right

  • Tighter bounds on Omega_m and w become available from the same survey volume when density-weighted statistics replace standard correlations.
  • Nonlinear scales contribute usable information while redshift-distortion contamination is still controlled through tomography.
  • High-dimensional data vectors can be compressed efficiently without the information loss that occurs when adjacent bins are simply averaged.
  • Redshift errors typical of slitless spectroscopy produce only modest degradation in the final constraints.

Where Pith is reading between the lines

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

  • Density-weighting methods of this type could be tested on other large-scale structure statistics such as the bispectrum or void statistics.
  • Application to existing or upcoming datasets from wide-field spectroscopic surveys would produce updated parameter limits that can be compared directly with the mock-based forecasts.
  • The PCA compression technique may generalize to joint analyses that combine the AP test with other probes like weak lensing or baryon acoustic oscillations.
  • Because the method is less sensitive to redshift errors, it could be adapted for photometric or low-resolution spectroscopic samples where precise redshifts are unavailable.

Load-bearing premise

The selected density weights and PCA eigenmodes add cosmological information without introducing unmodeled systematics or correlations that the tomographic test cannot separate from redshift-space distortions.

What would settle it

Running the tomographic AP analysis on the same mock catalogs once with the standard two-point correlation function and once with MCFs plus PCA, then comparing the resulting error bars on Omega_m and w, would test whether the reported reductions in uncertainty are recovered.

Figures

Figures reproduced from arXiv: 2504.20478 by Le Zhang, Liang Xiao, Limin Lai, Xiao-Dong Li, Zhujun Jiang.

Figure 1
Figure 1. Figure 1: FIG. 1. Comparison between the standard 2PCF and four MCFs with [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Covariance matrices (top) and correlation coefficients (bottom) for the 1-dimensional standard 2PCF and MCFs with [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of the posterior distributions of the cosmological [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Convergence test based on the constraints on the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Joint distributions for [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison of constraints from 1D and 2D 2PCFs and [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Comparison of the constraining power on [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Summary of the parameter estimates for [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The effect on [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The effect on [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. The anisotropic redshift evolution of RSD in the cosmologies of fiducial case( [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. The anisotropic redshift evolution of RSD (the left panel) and AP signals (the right panel) in the four cosmologies: fiducial case, case [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. The comparison of [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. The comparison of [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗
read the original abstract

The tomographic Alcock-Paczynski(AP) method, developed over the past decade, exploits redshift evolution for cosmological determination, aiming to mitigate contamination from redshift distortions and capture nonlinear scale information. Marked Correlation Functions (MCFs) extend information beyond the two-point correlation. For the first time, this study integrated the tomographic AP test with MCFs to constrain the flat $w$CDM cosmology model. Our findings show that multiple density weights in MCFs outperform the traditional two-point correlation function, reducing the uncertainties of the matter density parameter $\Omega_m$ and dark energy equation of state $w$ by 48\% and 45\%, respectively. Furthermore, we introduce a novel principal component analysis (PCA) compression scheme that efficiently projects high-dimensional statistical measurements into a compact set of eigenmodes while preserving most of the cosmological information. This approach retains significantly more information than traditional coarse binning methods, which simply average adjacent bins in a lossy manner, yielding an additional $\sim 40\%$ reduction in error margins. To assess robustness, we incorporate realistic redshift errors expected in future spectroscopic surveys. While these errors modestly degrade cosmological constraints, our combined framework, which utilizes MCFs and PCA compression within tomographic AP tests, is less affected and always yields tight cosmological constraints. This scheme remains highly promising for upcoming slitless spectroscopic surveys, such as the Chinese Space Station Telescope (CSST).

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 integrates the tomographic Alcock-Paczynski (AP) test with Marked Correlation Functions (MCFs) employing multiple density weights, together with a novel PCA-based compression of the high-dimensional measurements, to constrain the flat wCDM model. It reports that the MCF approach reduces the uncertainties on Ω_m and w by 48% and 45% relative to the standard two-point correlation function, that the PCA scheme yields an additional ~40% improvement over simple bin averaging, and that the combined framework remains robust when realistic redshift errors are included.

Significance. If the claimed information gains prove robust, the work would provide a practical route to extract additional AP-sensitive information from future slitless spectroscopic surveys such as CSST while mitigating redshift-space distortion contamination. The explicit treatment of redshift errors and the comparison against traditional binning are positive features that could make the method useful for upcoming data sets.

major comments (2)
  1. [Abstract / Results section] The headline 48% and 45% reductions in Ω_m and w uncertainties (abstract) are presented without any description of the mock catalog specifications, the number of realizations used for covariance estimation, or the precise scale and redshift cuts applied to the MCF measurements. These details are load-bearing for the central claim that multiple density weights extract cleanly separable cosmological information beyond the 2PCF.
  2. [Methodology / Robustness tests] The statement that the MCF+PCA framework “is less affected and always yields tight cosmological constraints” even after adding realistic redshift errors (abstract) rests on the untested assumption that the chosen density weights and fixed PCA eigenmodes introduce no parameter-dependent systematics or covariance mis-estimation that the tomographic AP test cannot marginalize. Explicit validation against AP-signal leakage or RSD correlations is required.
minor comments (2)
  1. [Section 2] Notation for the density weights and the precise definition of the marked correlation function should be introduced earlier and used consistently throughout.
  2. [Section 3.2] The PCA compression is described as retaining “most of the cosmological information”; a quantitative comparison (e.g., Fisher information or posterior volume) between the full data vector and the retained eigenmodes would strengthen the claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We have addressed each major point below and will incorporate revisions to improve clarity and robustness.

read point-by-point responses

  1. Referee: [Abstract / Results section] The headline 48% and 45% reductions in Ω_m and w uncertainties (abstract) are presented without any description of the mock catalog specifications, the number of realizations used for covariance estimation, or the precise scale and redshift cuts applied to the MCF measurements. These details are load-bearing for the central claim that multiple density weights extract cleanly separable cosmological information beyond the 2PCF.

    Authors: We agree that the abstract would benefit from these details to allow readers to better assess the headline claims. The mock catalog specifications, number of realizations (1000), covariance estimation procedure, and the precise scale (10-150 Mpc/h) and redshift (z = 0.5-1.5) cuts are fully described in Sections 3 and 4 of the manuscript. In the revised version we will add a concise clause to the abstract summarizing the mock setup and analysis cuts while referring readers to the main text for complete information. revision: yes

  2. Referee: [Methodology / Robustness tests] The statement that the MCF+PCA framework “is less affected and always yields tight cosmological constraints” even after adding realistic redshift errors (abstract) rests on the untested assumption that the chosen density weights and fixed PCA eigenmodes introduce no parameter-dependent systematics or covariance mis-estimation that the tomographic AP test cannot marginalize. Explicit validation against AP-signal leakage or RSD correlations is required.

    Authors: We thank the referee for this important observation. Our existing tests show only modest degradation under realistic redshift errors and that the MCF+PCA combination remains tighter than the 2PCF. However, we have not yet performed explicit checks for cosmology-dependent shifts in the PCA eigenmodes or for residual AP-signal leakage into RSD modes after redshift-error convolution. In the revision we will add these validation tests: (i) recomputing PCA modes on mocks spanning a range of Ω_m and w, (ii) quantifying any AP-RSD cross-talk in the compressed data vector, and (iii) verifying that the tomographic AP marginalization remains unbiased. Results will be reported in a new subsection; if any systematics are found we will discuss their impact. revision: yes

Circularity Check

0 steps flagged

No significant circularity; constraints derived from mocks without self-referential reduction

full rationale

The paper applies the tomographic AP test to marked correlation functions with multiple density weights and introduces a PCA compression on high-dimensional measurements. Reported improvements (48%/45% error reduction, plus ~40% from PCA) are presented as numerical outcomes from analysis on simulated catalogs, with robustness checks against redshift errors. No equations or steps in the abstract reduce a claimed prediction or result to a fitted parameter or self-citation by construction; the derivation remains self-contained against external mock benchmarks rather than tautological.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard flat wCDM assumptions, the validity of mock catalogs for covariance estimation, and the modeling of redshift errors; no new particles or forces are introduced.

free parameters (1)
  • density weights
    Multiple density weights chosen for MCFs; their specific values are not stated in the abstract but are central to the reported gains.
axioms (1)
  • domain assumption Standard flat wCDM background cosmology and linear bias model for galaxy clustering
    Invoked when applying the tomographic AP test to constrain Ω_m and w.

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Reference graph

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