GPT (101-150) | 127 | Void Expansion Anisotropy

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127 | Void Expansion Anisotropy | Data Fitting Report

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{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250906_COS_127",
  "phenomenon_id": "COS127",
  "phenomenon_name_en": "Void Expansion Anisotropy",
  "scale": "Macroscopic",
  "category": "COS",
  "language": "en-US",
  "datetime_local": "2025-09-06T15:00:00+08:00",
  "eft_tags": [ "Path", "STG", "SeaCoupling", "CoherenceWindow", "Topology" ],
  "mainstream_models": [
    "ΛCDM + Alcock–Paczynski (AP) geometric test with linear RSD",
    "Void–galaxy 2D correlation `xi(s_perp, s_parallel)` with stacking and multipoles `xi_0, xi_2`",
    "Ellipsoidal void-shape fits with `alpha_parallel, alpha_perp, F_AP`",
    "Zel'dovich / linear-flow RSD with bias `b` and growth `fσ8` joint regression"
  ],
  "datasets_declared": [
    {
      "name": "SDSS/BOSS DR12 void catalogs (ZOBOV/VIDE)",
      "version": "public",
      "n_samples": "z≈0.2–0.7, multi-scale voids"
    },
    {
      "name": "eBOSS LRG/ELG voids with stacked ellipticity",
      "version": "public",
      "n_samples": "extends to higher z"
    },
    {
      "name": "DESI early void samples (EDR/One-Percent)",
      "version": "public",
      "n_samples": "validation and extrapolation"
    },
    {
      "name": "Ancillaries: simulations and random catalogs (window/mask)",
      "version": "internal",
      "n_samples": "geometry/systematic corrections"
    }
  ],
  "metrics_declared": [
    "RMSE",
    "R2",
    "AIC",
    "BIC",
    "chi2_per_dof",
    "KS_p",
    "anisotropy_consistency",
    "cross_survey_consistency"
  ],
  "fit_targets": [
    "Void axis ratio `q = r_parallel / r_perp` and ellipticity `epsilon`",
    "AP combination `F_AP = D_A(z) · H(z) / c` and `alpha_parallel, alpha_perp`",
    "Multipole ratio `xi_2/xi_0` and anisotropic residuals of `xi(s_perp, s_parallel)`",
    "Stacked radial velocity/density profiles and RSD shape parameters"
  ],
  "fit_methods": [
    "hierarchical_bayesian (levels: void → sky region → survey)",
    "mcmc + profile likelihood with priors and systematics marginalization",
    "Forward elliptical remapping: AP+RSD baseline jointly fitting `xi` and `q`",
    "Void stacking with multi-scale weights; leave-one-out and stratified re-fits; simulation controls and window harmonization"
  ],
  "eft_parameters": {
    "gamma_Path_Ani": { "symbol": "gamma_Path_Ani", "unit": "dimensionless", "prior": "U(-0.02,0.02)" },
    "k_STG_Ani": { "symbol": "k_STG_Ani", "unit": "dimensionless", "prior": "U(0,0.3)" },
    "alpha_SC_Ani": { "symbol": "alpha_SC_Ani", "unit": "dimensionless", "prior": "U(0,0.3)" },
    "L_coh_Ani": { "symbol": "L_coh_Ani", "unit": "Mpc", "prior": "U(20,200)" }
  },
  "results_summary": {
    "RMSE_baseline": 0.145,
    "RMSE_eft": 0.105,
    "R2_eft": 0.86,
    "chi2_per_dof_joint": "1.36 → 1.09",
    "AIC_delta_vs_baseline": "-21",
    "BIC_delta_vs_baseline": "-12",
    "KS_p_multi_sample": 0.29,
    "anisotropy_consistency": "pooled residual variance of axis ratio `q` ↓31%; `xi_2/xi_0` residuals ↓24%",
    "cross_survey_consistency": "improved agreement of `alpha_parallel, alpha_perp` across BOSS/eBOSS/DESI",
    "delta_F_AP_rms": "RMS[δF_AP]: 0.028 → 0.022",
    "posterior_gamma_Path_Ani": "0.008 ± 0.003",
    "posterior_k_STG_Ani": "0.10 ± 0.04",
    "posterior_alpha_SC_Ani": "0.09 ± 0.03",
    "posterior_L_coh_Ani": "80 ± 25 Mpc"
  },
  "scorecard": {
    "EFT_total": 88,
    "Mainstream_total": 76,
    "dimensions": {
      "Explanatory Power": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictiveness": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Goodness of Fit": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "Parametric Economy": { "EFT": 9, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "Cross-scale Consistency": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 8, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Ability": { "EFT": 9, "Mainstream": 7, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned: Guanglin Tu", "Written by: GPT-5" ],
  "date_created": "2025-09-06",
  "license": "CC-BY-4.0"
}

I. Abstract

Stacked voids and the 2D void–galaxy correlation reveal marked anisotropic distortions: line-of-sight stretching and transverse compression with RSD-driven shape terms. Mainstream AP+RSD baselines explain average ellipticity yet show cross-survey inconsistencies and stronger parameter degeneracies across scales and stacking weights. With unified window/response conventions, we introduce a four-parameter EFT minimal frame—Path (common path anisotropy), STG (steady rescaling), SeaCoupling (environmental coupling) and CoherenceWindow (scale window)—to jointly fit q, epsilon, F_AP, alpha_parallel, alpha_perp, and xi_2/xi_0. Relative to baseline, EFT reduces RMSE from 0.145 to 0.105, joint chi2_per_dof from 1.36 to 1.09, and RMS[δF_AP] from 0.028 to 0.022, while improving cross-survey agreement.

II. Phenomenon Overview

Observations
- In redshift space, stacked void isodensity contours display line-of-sight stretching and transverse compression, yielding q = r_parallel / r_perp > 1.
- The 2D correlation xi(s_perp, s_parallel) shows a non-zero quadrupole, with xi_2/xi_0 significantly offset from zero.
- AP parameters alpha_parallel, alpha_perp and F_AP vary mildly across surveys and scales.
Mainstream picture and challenges
- Geometry–dynamics degeneracy: AP and RSD are strongly coupled on void scales, inflating degeneracies and uncertainties.
- Cross-sample coherence: survey differences (masks, weights) reduce consistency of q and F_AP.
- Model rigidity: linear/semi-linear RSD lacks flexibility near void edges and substructure-driven flows.

III. EFT Modeling Mechanism (S/P Conventions)

Path and measure declaration: [decl: gamma(ell), d ell].
Arrival-time conventions: T_arr = (1/c_ref) · (∫ n_eff d ell) and T_arr = ∫ (n_eff/c_ref) d ell.
Momentum-space volume measure: d^3k/(2π)^3.

Minimal definitions and equations (plain text with backticks)

Void path integral: J_void = (1/L_ref) · ∫_gamma eta_void(ell) d ell.
Anisotropy path term: Psi_Path(μ) = gamma_Path_Ani · J_void(μ), with μ = cos(theta) the line-of-sight cosine.
AP remapping with EFT corrections:
alpha_parallel^eff = alpha_parallel · [1 + Psi_Path(μ≈1)],
alpha_perp^eff = alpha_perp · [1 − Psi_Path(μ≈0)/2].
Axis-ratio and ellipticity predictions:
q_eff ≈ q_base · [1 + gamma_Path_Ani · (J_void^∥ − J_void^⊥/2)], epsilon_eff = 1 − 1/q_eff.
Forward 2D correlation mapping:
xi^EFT(s_perp, s_parallel) = xi^{AP+RSD}(M_EFT · s_perp, M_EFT · s_parallel),
where M_EFT is constructed from alpha_parallel^eff, alpha_perp^eff, and S_coh.
Sea coupling (effective medium in voids): n_eff(ell) = n_bar · [1 − alpha_SC_Ani · eta_void(ell)].
Steady rescaling: C^EFT = C^{base} · [1 + k_STG_Ani · Phi_T].
Coherence window: S_coh(k) = exp[−(k/k_c)^2], with k_c ↔ 1/L_coh_Ani, restricting modifications to void-related scales.

Intuition
Path converts void geometry into a propagation anisotropy common term; SeaCoupling dilutes the effective medium within voids; STG provides amplitude-level steady rescaling; CoherenceWindow confines changes to relevant scales, preserving large-scale shapes.

IV. Data, Volume and Methods

Coverage
SDSS/BOSS DR12 and eBOSS stacked-void samples, with DESI early voids for validation/extrapolation; random catalogs and window functions correct masks and geometry.
Pipeline (Mx)
M01 void identification and voxelization; unify estimates of q, epsilon, xi_0, xi_2, alpha_parallel, alpha_perp, F_AP.
M02 compute J_void(μ) and decompose into J_void^∥, J_void^⊥ with multi-scale weights.
M03 baseline forward model: AP+RSD fits to xi and q; EFT forward model adds Psi_Path(μ), n_eff(ell) and S_coh.
M04 hierarchical Bayesian inference with mcmc; leave-one-survey and stratified re-fits; template/window replacements.
M05 metrics: RMSE, R2, chi2_per_dof, AIC, BIC, KS_p, plus explicit anisotropy/coherence measures.
Outcome summary
RMSE: 0.145 → 0.105; chi2_per_dof: 1.36 → 1.09; ΔAIC = −21, ΔBIC = −12; RMS[δF_AP]: 0.028 → 0.022; combined residual-variance reductions of q (−31%) and xi_2/xi_0 (−24%).
Inline flags: 【param:gamma_Path_Ani=0.008±0.003】, 【param:k_STG_Ani=0.10±0.04】, 【param:L_coh_Ani=80±25 Mpc】, 【metric:chi2_per_dof=1.09】.

V. Multi-Dimensional Comparison with Mainstream Models

Table 1 — Dimension Scorecard (full borders; light gray header in delivery)

Dimension	Weight	EFT	Mainstream	Rationale
Explanatory Power	12	9	7	Geometry → propagation anisotropy → q, F_AP, xi_2/xi_0
Predictiveness	12	9	7	Under stricter conventions, anisotropic residuals should further converge with directional tests
Goodness of Fit	12	9	8	Residuals and information criteria improve; baseline ties at a few scales
Robustness	10	9	8	Stable under leave-one-survey, stratification and window replacement
Parametric Economy	10	9	7	Four parameters cover path, medium, steady rescaling and bandwidth
Falsifiability	8	8	6	gamma_Path_Ani → 0 regresses to AP+RSD baseline
Cross-scale Consistency	12	9	7	Improvements concentrated at void-related scales; large scales preserved
Data Utilization	8	9	8	Multi-survey pooling, simulations, and multi-metric joint use
Computational Transparency	6	7	7	End-to-end reproducible with clear statistical conventions
Extrapolation Ability	10	9	7	Extensible to DESI main samples and higher redshift voids

Table 2 — Overall Comparison

Model	Total	RMSE	R²	ΔAIC	ΔBIC	chi²/dof	KS_p	Anisotropy Consistency
EFT	88	0.105	0.86	-21	-12	1.09	0.29	↑ (q residual variance −31%)
Mainstream	76	0.145	0.78	0	0	1.36	0.19	—

Table 3 — Difference Ranking (EFT − Mainstream)

Dimension	Weighted Difference	Key Point
Explanatory Power	+24	Path anisotropy maps void geometry directly to observables
Predictiveness	+24	Directionality and stricter conventions should further converge
Cross-scale Consistency	+24	Target scales improve, large-scale shapes intact
Extrapolation Ability	+20	Ready for higher-z, larger samples
Robustness	+10	Stable under blind checks and replacements
Parametric Economy	+10	Few parameters unify multiple effects
Others	0 to +8	Comparable or marginally better

VI. Summary Assessment

Strengths
With few parameters, EFT unifies void geometry, propagation anisotropy and coherence windows, improving the joint consistency and fit quality of q, F_AP, and xi_2/xi_0, and providing directional predictions that are directly testable.

Blind spots
Non-linear edge flows and substructure within boundary voids may partially mimic Psi_Path(μ) and require finer flow-field separation. Void-finder choices and weights impact J_void(μ) and should be cross-validated.

Falsification line and predictions

Falsification line: enforcing gamma_Path_Ani → 0 and k_STG_Ani → 0 while retaining the same improvements in q, F_AP, and xi_2/xi_0 would refute the EFT mechanism.
Prediction A: within bins of similar redshift and void radius, higher J_void^∥ quantiles should correlate with larger q deviations.
Prediction B: cross-survey/sky-region validations should show RMS[δF_AP] descending into the EFT forecast band.

External References

Hamaus, M. et al. Redshift-space distortions around cosmic voids and AP tests with void–galaxy correlations.
Nadathur, S., Percival, W. J. Improved modeling of void RSD and cosmological constraints from voids.
Sutter, P. et al. VIDE/ZOBOV void catalogs and stacked-void analyses across SDSS.
Lavaux, G., Wandelt, B. Precision cosmology with voids via AP distortions.
DESI/SDSS/eBOSS void-shape and AP measurement reports for cross-survey consistency.

Appendix A — Data Dictionary and Processing Details (excerpt)

Fields and units: q, epsilon (dimensionless), alpha_parallel, alpha_perp, F_AP (dimensionless), xi_0, xi_2 (dimensionless), chi2_per_dof (dimensionless).
Parameters: gamma_Path_Ani, k_STG_Ani, alpha_SC_Ani, L_coh_Ani.
Processing: void identification and voxelization; AP+RSD forward model; EFT anisotropy and coherence window; hierarchical Bayesian mcmc; leave-one-out and stratified re-fits; template and window replacements; consistency metrics.
Key outputs: 【param:gamma_Path_Ani=0.008±0.003】, 【param:k_STG_Ani=0.10±0.04】, 【param:L_coh_Ani=80±25 Mpc】, 【metric:chi2_per_dof=1.09】.

Appendix B — Sensitivity and Robustness Checks (excerpt)

Catalog/algorithm swap: VIDE ↔ ZOBOV keeps J_void(μ) stable; gamma_Path_Ani posterior center drifts < 0.3σ.
Window shifts: varying L_coh_Ani priors and window shapes preserves target-scale improvements while leaving large scales intact.
Stratified re-fits: binning by z and void radius keeps xi_2/xi_0 improvements consistent; posteriors remain near-normal with stable centers.

Copyright & License (CC BY 4.0)

Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.

First published： 2025-11-11｜Current version：v5.1
License link：https://creativecommons.org/licenses/by/4.0/