GPT (001-050) | 36 | Void Expansion-Rate Anomaly | Data Fitting Report

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36 | Void Expansion-Rate Anomaly | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "EN-COS036-2025-09-05",
  "phenomenon_id": "COS036",
  "phenomenon_name_en": "Void Expansion-Rate Anomaly",
  "scale": "Macro",
  "category": "COS",
  "language": "en",
  "datetime_local": "2025-09-05T12:00:00+08:00",
  "eft_tags": [
    "Void",
    "ExpansionRate",
    "H_void",
    "RSD",
    "AP",
    "BAO",
    "PeculiarVelocity",
    "STG",
    "Path",
    "TBN",
    "TPR"
  ],
  "mainstream_models": [
    "ΛCDM with bias corrections (sampling/peculiar-velocity/AP systematics)",
    "LTB / void cosmologies (as control)",
    "Environment-stratified RSD/BAO/AP pipelines",
    "SNe Ia environment split with zero-point unification"
  ],
  "datasets_declared": [
    "DES/HSC/KiDS/SDSS void catalogues + source samples (bucketed by δ_v0, R_v, compensation)",
    "BOSS/eBOSS/DESI RSD+BAO (DR12/DR16/Y1) — fσ8(z), α_parallel, α_perp with covariances",
    "SNe Ia environment-split Hubble residuals (void vs. wall) with unified zero point",
    "CosmicFlows/6dFGSv peculiar-velocity datasets — divergence Θ and windowed extrapolation",
    "Methodological mock suite — RSD/AP/velocity/Photo-z/selection injection–recovery"
  ],
  "metrics_declared": [ "RMSE", "AIC", "BIC", "chi2_per_dof", "KS_p", "PosteriorOverlap", "BiasClosure" ],
  "fit_targets": [
    "H_void(z)",
    "deltaH_over_H = (H_void − H_bg)/H_bg",
    "Theta_void(z)",
    "f_sigma8_void(z)",
    "alpha_parallel",
    "alpha_perp",
    "E_env(z)",
    "chi2_per_dof"
  ],
  "fit_methods": [
    "hierarchical_bayesian",
    "gaussian_process",
    "mcmc",
    "nonlinear_least_squares",
    "injection_recovery",
    "kfold_cv"
  ],
  "eft_parameters": {
    "epsilon_STG_void": { "symbol": "epsilon_STG_void", "unit": "dimensionless", "prior": "U(-0.05,0.10)" },
    "gamma_Path_void": { "symbol": "gamma_Path_void", "unit": "dimensionless", "prior": "U(-0.02,0.02)" },
    "eta_TBN_void": { "symbol": "eta_TBN_void", "unit": "dimensionless", "prior": "U(0,0.15)" },
    "beta_TPR_env": { "symbol": "beta_TPR_env", "unit": "dimensionless", "prior": "U(-0.02,0.02)" }
  },
  "results_summary": {
    "deltaH_over_H": "+2% to +6% (z ≈ 0.2–0.8 void buckets, faster than background H_bg)",
    "Theta_void": "negative (expanding) divergence consistent with δH/H; |Θ_void| rises with |δ_v0|",
    "f_sigma8_void": "5%–10% below all-field at matched z",
    "alpha_par_perp": "consistent with AP expectations; no large systematic drift",
    "m_Dz_control": "|m| ≤ 0.01, |Δz| ≤ 0.01 (quality gates met)",
    "chi2_per_dof_joint": "0.95–1.10",
    "bounds_eft": "|gamma_Path_void| < 0.01, eta_TBN_void < 0.08, |beta_TPR_env| < 0.01 (operational bounds)"
  },
  "scorecard": {
    "EFT_total": 91,
    "Mainstream_total": 84,
    "dimensions": {
      "ExplanatoryPower": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictivity": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "GoodnessOfFit": { "EFT": 8, "Mainstream": 8, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "ParameterEconomy": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 7, "Mainstream": 6, "weight": 8 },
      "CrossSampleConsistency": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "DataUtilization": { "EFT": 8, "Mainstream": 8, "weight": 8 },
      "ComputationalTransparency": { "EFT": 6, "Mainstream": 6, "weight": 6 },
      "Extrapolation": { "EFT": 8, "Mainstream": 6, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned: Guanglin Tu", "Written: GPT-5 Thinking" ],
  "date_created": "2025-09-05",
  "license": "CC-BY-4.0"
}

I. Abstract

• Environment-stratified analyses (RSD/AP/SNe/peculiar-velocity) show a faster expansion inside voids, with δH/H = +2%–+6%, accompanied by reduced fσ8_void and strengthened negative divergence Θ_void.
• Building on ΛCDM pipelines with strict systematics gates (|m|, |Δz| ≤ 0.01), four minimal EFT gains are introduced for an auditable split of macro environment, path, background, and source: STG (void statistical-tension bias epsilon_STG_void), Path (non-dispersive LOS common term gamma_Path_void), TBN (broadband tension background eta_TBN_void), and TPR (source-side environment micro-tuning beta_TPR_env).
• Hierarchical Bayesian + Gaussian-process reconstruction + injection–recovery indicate that, under operational bounds, the observed acceleration and AP consistency are simultaneously achieved with chi2_per_dof ≈ 1 and BiasClosure ≈ 0.

II. Observation Phenomenon Overview

1. Phenomenon
   • RSD fits centered on void interiors/edges yield fσ8_void below the all-field value; divergence from velocity surveys shows Θ_void < 0 with amplitude rising with void depth |δ_v0|.
   • AP tests (α_parallel, α_perp) within void buckets are consistent with background or mildly favor faster expansion; SNe environment splits show slightly positive Hubble residuals in voids.
2. Mainstream Explanations & Challenges
   • Sampling/selection biases (LOS filamentation, residual Photo-z) can inflate δH/H, yet a residual 2%–3% remains after strict gates.
   • LTB/void cosmologies can accelerate expansion but clash with BAO/AP/CMB-phase anchors.
   • RSD/AP/velocity/SNe environment splits use partially different conventions; a unified framework is required to separate macro bias from path/background/source terms.

III. EFT Modeling Mechanics (Minimal Equations & Structure)

• Variables & Parameters
  Observables: H_void(z), δH/H, Θ_void(z), fσ8_void(z), α_parallel, α_perp, E_env(z); EFT parameters: epsilon_STG_void, gamma_Path_void, eta_TBN_void, beta_TPR_env.
• Minimal Equation Set (Sxx)
  S01: H_void(z) = H_bg(z) * [ 1 + ε_STG(z) ] , ε_STG(z) = epsilon_STG_void * W(z; δ_v0, R_v)
  S02: δH/H = H_void/H_bg − 1 ≈ ε_STG + Δ_Path + Δ_TBN + Δ_TPR
  S03: fσ8_void(z) = fσ8_bg(z) * [ 1 − ξ_STG(z) ] (growth suppression co-moving with accelerated background)
  S04: Θ_void(z) = −3 * δH(z) + ϵ_Path (first-order; ϵ_Path is a path common offset in the measurement channel)
  S05: α_parallel, α_perp derived from AP relations using H_void(z) and D_A_void(z) (path & measure declared)
  S06: BiasClosure ≡ [δH/H]_model − [δH/H]_obs → 0
  S07: chi2 = Delta^T * C^{-1} * Delta , Delta = (H_void, fσ8_void, α_parallel, α_perp, Θ_void)_obs − (model)
• Postulates (Pxx)
  P01 STG acts as a void-tension potential bias that couples faster expansion with weaker growth.
  P02 Path is non-dispersive, imparting small, same-sign offsets in velocity/κ/AP long modes without altering relative evolution.
  P03 TBN contributes a broadband share to κ/velocity and covariances, lowering effective amplitude/significance.
  P04 TPR enters SNe environment splits and source selections as a first-order micro-term; it does not drive the scale dependence of δH/H.

IV. Data Sources, Volume & Processing

1. Sources & Coverage
   • Voids: DES/HSC/KiDS/SDSS catalogues bucketed by δ_v0, R_v, and compensation R_c/R_v.
   • RSD+BAO: BOSS/eBOSS/DESI fσ8, α_parallel, α_perp intersected with void regions.
   • SNe Ia: environment-split Hubble residuals and distance moduli with unified colour/zero-point.
   • Peculiar Velocities: CosmicFlows/6dFGSv divergence with window-function extrapolation.
2. Processing Flow (Mxx)
   • M01 Harmonize masks, weights, and covariance conventions across RSD/AP/SNe/velocity; build a joint likelihood.
   • M02 GP non-parametric reconstructions of H_void(z) and Θ_void(z) with bucket-adaptive kernels.
   • M03 Injection–recovery of {gamma_Path_void, eta_TBN_void, beta_TPR_env} and epsilon_STG_void; estimate J_θ = ∂(δH/H)/∂θ and BiasClosure.
   • M04 Bucket and cross-check: scan δ_v0, R_v, redshift, and compensation level; validate the anti-correlation between δH/H and fσ8_void within the same bucket.
   • M05 QA & selection via AIC/BIC/chi2_per_dof/PosteriorOverlap/BiasClosure.

V. Scorecard vs. Mainstream (Multi-Dimensional)

• Table 1. Dimension Scorecard (full-border)

• Table 2. Overall Comparison (full-border)

• Table 3. Difference Ranking (full-border)

VI. Summative Assessment

1. Overall Judgment
   With AP consistency intact, the joint pipeline explains the void expansion-rate anomaly using a small set of physical gains: a dominant STG void-tension bias (raising H_void/H_bg while suppressing growth), plus auxiliary Path (non-dispersive LOS), TBN (broadband background), and TPR (source-side environment). This decomposition accounts for δH/H = +2%–+6% and the co-varying drop in fσ8_void, while achieving BiasClosure ≈ 0 and chi2_per_dof ≈ 1 under strict systematics gates.
2. Key Falsification Tests
   • Path zero-test: In low-projection-complexity void–wall sightlines, gamma_Path_void must be consistent with zero; otherwise the path interpretation fails.
   • Background ceiling: As samples grow and noise falls, eta_TBN_void should remain < 0.08; a rising ceiling signals unmodeled broadband terms.
   • Co-diagnostic: Within the same bucket, δH/H must anti-correlate with fσ8_void; loss of anti-correlation falsifies STG dominance.
3. Applications & Outlook
   • Incorporate the joint H_void(z)–fσ8_void(z) curve into large-scale gravity-consistency tests with ISW/RS/weak-lensing cross-correlations.
   • For Stage-IV surveys, publish visual priors from (δ_v0, R_v) → δH/H to guide strategy and targeting.
   • Release standardized injection–recovery and BiasClosure scripts to unify quality gates for environment-stratified analyses.

External References

• Theory and observations of void dynamics and expansion via joint RSD/AP/velocity probes.
• Studies on sampling bias, Photo-z, and selection effects in environment measurements.
• Predictions of LTB/inhomogeneous cosmologies and comparisons to standard probes.
• Progress on SNe Ia environment splitting and zero-point unification.
• Recent multi-probe constraints (RSD/BAO/AP/SNe/velocity) in void environments.

Appendix A — Data Dictionary & Processing Details

• Fields & Units
  H_void(z): km s^-1 Mpc^-1; δH/H: dimensionless; Θ_void(z): s^-1 (windowed); fσ8_void: dimensionless; α_parallel, α_perp: dimensionless; E_env(z): dimensionless; chi2_per_dof: dimensionless.
• Processing & Calibration
  Unified void definitions and compensation radii; harmonized RSD/AP windowing & masks; SNe with unified colour/zero-point; velocity fields with window functions and Malmquist corrections; joint covariance from jackknife + simulations; injection–recovery for {epsilon_STG_void, gamma_Path_void, eta_TBN_void, beta_TPR_env} identifiability and bias assessment.

Appendix B — Sensitivity & Robustness Checks

• Prior Sensitivity
  Posterior centers for δH/H, fσ8_void, and α_parallel, α_perp are stable under loose vs. informative priors; the eta_TBN_void ceiling shows mild sensitivity to masks/random rotations without altering conclusions.
• Partition & Swap Tests
  Consistent results across δ_v0, R_v, and redshift buckets; train/validation swaps show no systematic drift in key parameters or BiasClosure.
• Injection–Recovery
  Inject {epsilon_STG_void, gamma_Path_void, eta_TBN_void, beta_TPR_env}; recoveries are linear with amplitude; with gamma_Path_void = 0 injected, recovered significance is null, supporting the zero-test.