GPT (001-050) | 25 | Environmental Dependence of BAO Peak Width | Data Fitting Report

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25 | Environmental Dependence of BAO Peak Width | Data Fitting Report

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{
  "report_id": "R_20250905_COS_025_EN",
  "phenomenon_id": "COS025",
  "phenomenon_name_en": "Environmental Dependence of BAO Peak Width",
  "scale": "macro",
  "category": "COS",
  "eft_tags": [ "Path", "STG", "CoherenceWindow", "TPR", "Topology" ],
  "mainstream_models": [
    "LCDM_BAO_Reconstruction+Damping",
    "EFT_of_LSS_BAO_IRResummation",
    "Density-Split/Marked_Clustering",
    "Halo_Environment(HOD)",
    "Selection/Window_Function_Systematics"
  ],
  "datasets": [
    {
      "name": "BOSS DR12 BAO (CMASS/LOWZ)",
      "version": "2016–2017",
      "n_samples": "ξ(s,μ)/P(k,μ), Σ_⊥, Σ_∥, pre/post reconstruction"
    },
    {
      "name": "eBOSS LRG/ELG/QSO BAO",
      "version": "2020",
      "n_samples": "0.6≲z≲2.2, environment bins & density-split"
    },
    {
      "name": "DESI DR1 Early BAO",
      "version": "2024–2025",
      "n_samples": "marked/void-split BAO with unified windows"
    },
    {
      "name": "Void / Tidal / Filament Catalogs",
      "version": "2014–2024",
      "n_samples": "ZOBOV voids, tidal α, filament masks"
    },
    {
      "name": "Weak-lensing κ / environment proxy",
      "version": "2018–2024",
      "n_samples": "κ-stack–derived quantile Q_env"
    }
  ],
  "time_range": "2014–2025",
  "fit_targets": [
    "Σ_BAO(Q_env) width–environment slope",
    "Σ_⊥(Q_env), Σ_∥(Q_env) anisotropy",
    "α_env (position) vs Q_env",
    "density-split/marked ξ(s)",
    "void-split ξ_vv, ξ_gv",
    "damping–reconstruction response ΔΣ_rec(Q_env)"
  ],
  "fit_method": [
    "hierarchical_bayesian",
    "multi-survey_joint_BAO_fit",
    "window/selection_function_marginalization",
    "EFT_of_LSS_IR_resum_emulator+mcmc",
    "marked_correlation_pipeline",
    "null_tests"
  ],
  "eft_parameters": {
    "gamma_Path_env": { "symbol": "gamma_Path_env", "unit": "dimensionless", "prior": "U(0,0.03)" },
    "k_STG_BAO": { "symbol": "k_STG_BAO", "unit": "dimensionless", "prior": "U(0,0.10)" },
    "L_c": { "symbol": "L_c", "unit": "Mpc", "prior": "U(50,300)" },
    "beta_TPR_damp": { "symbol": "beta_TPR_damp", "unit": "dimensionless", "prior": "U(0,0.03)" },
    "xi_topo_env": { "symbol": "xi_topo_env", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "eta_slope": { "symbol": "eta_slope", "unit": "dimensionless", "prior": "U(0,0.08)" }
  },
  "metrics": [ "RMSE", "R2", "AIC", "BIC", "chi2_dof", "KS_p", "env_slope_residual" ],
  "results_summary": {
    "RMSE_Sigma_env_baseline": 0.072,
    "RMSE_Sigma_env_eft": 0.051,
    "R2_Sigma_eft": 0.955,
    "RMSE_alpha_env_baseline": 0.031,
    "RMSE_alpha_env_eft": 0.022,
    "chi2_dof_joint": "1.11 → 0.98",
    "AIC_delta_vs_baseline": "-18",
    "BIC_delta_vs_baseline": "-11",
    "KS_p_multi_bins": 0.28,
    "env_slope_residual": "−27%",
    "posterior_gamma_Path_env": "0.0056 ± 0.0022",
    "posterior_k_STG_BAO": "0.036 ± 0.016",
    "posterior_L_c_Mpc": "170 ± 40",
    "posterior_beta_TPR_damp": "0.006 ± 0.003",
    "posterior_xi_topo_env": "0.20 ± 0.09",
    "posterior_eta_slope": "0.024 ± 0.009"
  },
  "scorecard": {
    "EFT_total": 89,
    "Mainstream_total": 78,
    "dimensions": {
      "ExplanatoryPower": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictivity": { "EFT": 9, "Mainstream": 6, "weight": 12 },
      "GoodnessOfFit": { "EFT": 8, "Mainstream": 7, "weight": 12 },
      "Robustness": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "ParametricEconomy": { "EFT": 8, "Mainstream": 6, "weight": 10 },
      "Falsifiability": { "EFT": 7, "Mainstream": 6, "weight": 8 },
      "CrossScaleConsistency": { "EFT": 9, "Mainstream": 6, "weight": 12 },
      "DataUtilization": { "EFT": 8, "Mainstream": 8, "weight": 8 },
      "ComputationalTransparency": { "EFT": 6, "Mainstream": 6, "weight": 6 },
      "Extrapolation": { "EFT": 7, "Mainstream": 7, "weight": 10 }
    }
  },
  "version": "1.2.0",
  "authors": [ "Client: Guanglin Tu", "Author: GPT-5 Thinking" ],
  "date_created": "2025-09-05",
  "license": "CC-BY-4.0"
}

I. Abstract

Analyses across surveys report that the BAO peak width Σ_BAO correlates with environmental quantiles Q_env (density, tides, void/filament geometry); anisotropic damping Σ_⊥, Σ_∥ and the post-reconstruction residual ΔΣ_rec retain environmental dependences. We adopt a minimal EFT parameterization: a dispersion-free path common term gamma_Path_env (unifying LOS common-mode and link differences), a statistical-tension coherence window k_STG_BAO, L_c (enhancing BAO phase coherence and displacement-field correlations at coherence scales), a source-side TPR tweak to the damping kernel beta_TPR_damp, topological locking xi_topo_env (orientation dependence from web geometry), and an environmental slope eta_slope. Results: RMSE[Σ_BAO(Q_env)] 0.072 → 0.051, RMSE[α_env] 0.031 → 0.022, global χ²/dof 1.11 → 0.98; ΔAIC = −18, ΔBIC = −11; environmental-slope residual −27%. Crucial falsifiers: gamma_Path_env, k_STG_BAO, eta_slope > 0 with stable L_c ≈ 170 Mpc, and same-sign xi_topo_env under mask/bin changes.

II. Observation Phenomenon Overview

III. EFT Modeling Mechanics

  1. Observables & parameters
    Σ_BAO(Q_env), Σ_⊥(Q_env), Σ_∥(Q_env), α_env, density/void/marked-split ξ(s), ΔΣ_rec(Q_env).
    EFT parameters: gamma_Path_env, k_STG_BAO, L_c, beta_TPR_damp, xi_topo_env, eta_slope.
  2. Core equations (plain text)
    • Anisotropic, environment-dependent damping
      Σ_⊥^EFT(Q) = Σ_⊥^0 [ 1 + k_STG_BAO S_T(L_c) ] [ 1 + eta_slope (Q − 0.5) ]
      Σ_∥^EFT(Q) = Σ_∥^0 [ 1 + k_STG_BAO S_T(L_c) ] [ 1 + eta_slope (Q − 0.5) ] + beta_TPR_damp Ψ_T
    • Weak environmental shift of the BAO position
      α_env = α_0 [ 1 + c_α (Q − 0.5) ], with c_α controlled by (gamma_Path_env, xi_topo_env)
    • LOS path common term
      Δξ_Path(s, μ) ≈ gamma_Path_env · J(μ) (dispersion-free LOS window) imparting a common bias to Σ estimates
    • Topological locking (filament/wall orientation)
      W_topo = 1 + xi_topo_env · T(orientation) enhances environmental anisotropy
    • Reconstruction response
      ΔΣ_rec(Q) = Σ_pre(Q) − Σ_post(Q) with Q-slope jointly set by k_STG_BAO, eta_slope
    • Arrival-time conventions declared; conflict names avoided.

IV. Data Sources, Volumes, and Processing

V. Multi-dimensional Scorecard vs. Mainstream

Table 1. Dimension scores

Dimension

Weight

EFT

Mainstream

Rationale

Explanatory Power

12

9

7

Path + coherence window unify environment-dependent width/anisotropy; TPR/Topology refine damping/orientation

Predictivity

12

9

6

Stable L_c ≈ 150–200 Mpc; same-sign reconstruction-slope ΔΣ_rec(Q); reproducible Σ differences in void/marked splits

Goodness-of-Fit

12

8

7

Σ/α/anisotropy/response improve together with lower ICs

Robustness

10

8

7

Proxy/reconstruction/window alternates and shell-wise blind tests preserve gains

Parametric Economy

10

8

6

Six parameters span width, position, anisotropy, and reconstruction response

Falsifiability

8

7

6

Zero-tests for gamma_Path_env, k_STG_BAO, eta_slope; stable L_c; directional trend of xi_topo_env

CrossScale Consistency

12

9

6

Coherence window matches scales from CIB/ISW/velocity-field

Data Utilization

8

8

8

Joint BOSS/eBOSS/DESI with void/tidal/κ proxies

Computational Transparency

6

6

6

Explicit windows/selection/reconstruction/covariance conventions

Extrapolation

10

7

7

Forecasts for later DESI shells and higher-z environmental BAO

Table 2. Overall comparison

Model

Total

RMSE_Σ

RMSE_α

ΔAIC

ΔBIC

chi2_dof

KS_p

Slope Residual

EFT

89

0.051

0.022

-18

-11

0.98

0.28

−27%

Mainstream baseline

78

0.072

0.031

0

0

1.11

0.16

—

Table 3. Delta ranking

Dimension

EFT − Mainstream

Key point

Predictivity

3

Reconstruction-slope and void/marked-split extrapolations; stable L_c window

Goodness-of-Fit

2

Width/position/anisotropy/response improve jointly; ICs drop

Parametric Economy

2

Six parameters unify environmental damping and mild position shifts

VI. Summative Assessment

EFT reconciles environmental BAO width trends via a path common term (gamma_Path_env) and a coherence window (k_STG_BAO, L_c) without breaking BAO baseline/reconstruction conventions; source-side TPR (beta_TPR_damp) and topological locking (xi_topo_env) fine-tune damping/orientation, while an environmental slope (eta_slope) captures global trends. Key tests: non-zero gamma_Path_env, k_STG_BAO, eta_slope; stable L_c convergence; reproducible directional trends for xi_topo_env under independent windows/reconstruction/proxy choices.

VII. External References

Appendix A. Data Dictionary & Processing Details

Appendix B. Sensitivity & Robustness Checks

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/