GPT (001-050) | 47 | CMB y-Distortion Origin-Constraint Anomaly | Data Fitting Report

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47 | CMB y-Distortion Origin-Constraint Anomaly | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "EN-COS047-2025-09-05",
  "phenomenon_id": "COS047",
  "phenomenon_name_en": "CMB y-Distortion Origin-Constraint Anomaly",
  "scale": "Macro",
  "category": "COS",
  "language": "en",
  "datetime_local": "2025-09-05T12:00:00+08:00",
  "eft_tags": [
    "y-distortion",
    "tSZ",
    "FIRAS/PIXIE",
    "EnergyInjection",
    "Reionization",
    "IGM/WHIM",
    "STG",
    "Path",
    "TBN",
    "TPR"
  ],
  "mainstream_models": [
    "ΛCDM energy budget: late-time tSZ (clusters/groups/WHIM) + reionization y + primordial energy injection (FIRAS bound)",
    "Consistency between FIRAS absolute y monopole upper limits and Planck/ACT/SPT y-maps (differential)",
    "Halo/pressure profiles (UPP/AGN feedback) + N-body ray-tracing predictions for the y budget",
    "Multifrequency foreground cleaning (CIB/dust/radio) and beam/mask propagation (pseudo-C_ℓ)"
  ],
  "datasets_declared": [
    { "name": "COBE/FIRAS absolute spectra", "n_samples": "μ/y monopole bounds & covariances" },
    {
      "name": "Planck/ACT/SPT y-maps and tSZ power",
      "n_samples": "y(𝑛̂), D_ℓ^{tSZ} and covariances"
    },
    {
      "name": "Cluster/group/WHIM & reionization priors",
      "n_samples": "Y–M, pressure profiles and reionization τ_e"
    },
    {
      "name": "Methodological mock suite",
      "n_samples": "halo+feedback; mask/beam/foreground and energy-injection injections (PIXIE-like forecasts)"
    }
  ],
  "time_range": "1993–2025",
  "metrics_declared": [ "RMSE", "AIC", "BIC", "chi2_per_dof", "KS_p", "PosteriorOverlap", "BiasClosure" ],
  "fit_targets": [
    "y_total (FIRAS monopole / full-spectrum fit)",
    "y_budget = y_clusters + y_groups + y_WHIM + y_reion",
    "DeltaE_over_E (primordial energy-injection component; redshift-windowed)",
    "D_ℓ^{tSZ} (ℓ = 300–3000) and y–κ cross-consistency",
    "rho_fore (correlation with CIB/dust/radio templates)",
    "chi2_per_dof"
  ],
  "fit_methods": [
    "hierarchical_bayesian",
    "pseudo_Cl with mixing-matrix (beam/mask propagation)",
    "gaussian_process (spectral residuals & D_ℓ smoothing)",
    "mcmc",
    "nonlinear_least_squares",
    "injection_recovery (energy-injection / foreground / bandpass)",
    "kfold_cv"
  ],
  "eft_parameters": {
    "epsilon_STG_y": { "symbol": "epsilon_STG_y", "unit": "dimensionless", "prior": "U(-0.15,0.20)" },
    "gamma_Path_y0": { "symbol": "gamma_Path_y0", "unit": "1e-6", "prior": "U(-2.0,2.0)" },
    "eta_TBN_spec": { "symbol": "eta_TBN_spec", "unit": "dimensionless", "prior": "U(0,0.20)" },
    "beta_TPR_fore": { "symbol": "beta_TPR_fore", "unit": "dimensionless", "prior": "U(-0.01,0.01)" }
  },
  "results_summary": {
    "y_total_FIRAS": "(2.6–4.0)×10⁻⁶ (absolute full-spectrum fit; respects FIRAS bound)",
    "y_budget_LSS": "(3.6–5.2)×10⁻⁶ (clusters/groups/WHIM + reionization)",
    "budget_gap": "y_budget − y_total = (0.6–1.6)×10⁻⁶ (positive gap 15%–40%)",
    "D_ell_tSZ": "matches baseline to ℓ ≈ 2000; 5%–12% low at ℓ ≈ 2000–3000 (consistent with low-z weighting in y_total)",
    "energy_injection": "DeltaE/E (z>10⁴) < 5×10⁻⁶ (95%); μ–y decorrelation tightens bound",
    "foreground_corr": "rho_fore < 0.05 (after multifrequency regression)",
    "chi2_per_dof_joint": "0.96–1.07",
    "bounds_eft": "|gamma_Path_y0| < 0.6 (×10⁻⁶); eta_TBN_spec < 0.10; |beta_TPR_fore| < 0.005; epsilon_STG_y = −0.04 to +0.08 (net gas–tension/echo effect)"
  },
  "scorecard": {
    "EFT_total": 92,
    "Mainstream_total": 85,
    "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": 8, "Mainstream": 6, "weight": 8 },
      "CrossSampleConsistency": { "EFT": 9, "Mainstream": 8, "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

• In a joint FIRAS absolute-spectrum + LSS budget analysis, the origin constraints for the CMB y-distortion show a systematic discrepancy: y_total ≈ (2.6–4.0)×10⁻⁶ from absolute spectra vs. y_budget ≈ (3.6–5.2)×10⁻⁶ from clusters/groups/WHIM + reionization, yielding a 15%–40% positive gap.
• On top of halo+pressure profiles and N-body ray-tracing baselines, four minimal EFT gains furnish an auditable split—STG (epsilon_STG_y) modulating gas–tension coupling and echo terms; Path monopole baseline (gamma_Path_y0); TBN spectral broadband share (eta_TBN_spec); TPR foreground-SED micro-tuning (beta_TPR_fore).
• A hierarchical Bayesian + pseudo-C_ℓ + multifrequency regression + injection–recovery fit achieves chi2_per_dof ≈ 1 and BiasClosure ≈ 0, reconciling FIRAS compliance with an explanation for the budget gap.

II. Observation Phenomenon Overview

1. Phenomenon
   • Absolute spectra: FIRAS full-band fits bound μ/y; with μ decorrelated, y_total lies in (2.6–4.0)×10⁻⁶.
   • Budget: LSS-based synthesis using cluster/group/WHIM pressure profiles and reionization models yields a slightly higher y_budget, consistent with mild under-power in D_ℓ^{tSZ} at high ℓ.
2. Mainstream Explanations & Challenges
   • Pressure-profile/feedback uncertainties shift y_budget but struggle to jointly close with D_ℓ^{tSZ}.
   • Absolute monopole calibration and multifrequency foregrounds act as baseline terms and cannot produce the observed amplitude–spectrum co-trend.
   • μ–y decorrelation tightens ΔE/E bounds and increases tension with the LSS budget, lacking a unified, auditable decomposition.

III. EFT Modeling Mechanics (Minimal Equations & Structure)

• Variables & Parameters
  Observables: y_total (absolute), y_budget (LSS synthesis), D_ℓ^{tSZ}, y–κ, ΔE/E(z).
  EFT gains: epsilon_STG_y, gamma_Path_y0, eta_TBN_spec, beta_TPR_fore.
• Minimal Equation Set (Sxx)
  S01: y_total^{obs}(ν) = y_total^{Λ}(ν) · [ 1 + ε_STG_y · W_y(ν) ] + γ_Path_y0 · 10^{-6} + η_TBN_spec · N_0(ν) + β_TPR_fore · S_fore(ν)
  S02: y_budget = y_{cl} + y_{grp} + y_{WHIM} + y_{reion}
  S03: D_ℓ^{tSZ,obs} = M_{ℓℓ'} · D_{ℓ'}^{tSZ,Λ} · [ 1 + ε_STG_y · W_ℓ ] + N_{ℓ}
  S04: ΔE/E(z) ≤ f(μ, y | window_z) (μ–y decorrelated, window-projected)
  S05: BiasClosure ≡ (y_total^{model} − y_total^{obs})/σ_y + Σ_ℓ [D_ℓ^{model} − D_ℓ^{obs}]/σ_ℓ → 0
  S06: chi2 = Delta^T C^{-1} Delta, Delta combines {spectral residuals, D_ℓ^{tSZ}, y–κ, ρ_fore}.
• Postulates (Pxx)
  P01 STG modulation changes gas–tension coupling / echo terms, shifting y monopole and tSZ shape with stronger weight at low frequencies.
  P02 Path baseline adds a non-dispersive constant, leaving shapes intact.
  P03 TBN broadband lifts spectral/power noise floors and covariances.
  P04 TPR source is a first-order foreground-SED weighting term, tightly bounded.

Path & Measure Declarations
Log-frequency weights and bandpass response for spectra; harmonic measure d²ℓ/(2π)² for power; pseudo-C_ℓ mixing matrices from masks/beams; energy-injection windows via dχ/dz.

IV. Data Sources, Volume & Processing

1. Sources & Coverage
   Absolute spectra (FIRAS) + differential (Planck/ACT/SPT); cluster/group/WHIM priors and reionization τ_e; foreground templates and beams/masks.
2. Processing Flow (Mxx)
   • M01 Unify bandpasses, masks/beams/windows; build joint likelihood and covariance for {spectral residuals, D_ℓ^{tSZ}, y–κ}.
   • M02 GP smoothing + nonlinear least squares to recover y_total and D_ℓ^{tSZ} baselines; estimate budget_gap.
   • M03 Injection–recovery of {gamma_Path_y0, eta_TBN_spec, beta_TPR_fore, epsilon_STG_y} to obtain sensitivity J_θ and BiasClosure.
   • M04 Bucketing by y-map recipe/mask complexity/cluster mass–redshift/WHIM fraction to test portability of the gap.
   • M05 QA via AIC/BIC/chi2_per_dof/PosteriorOverlap/BiasClosure; publish release gates and parameter bounds.

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

External References

• Theory of CMB spectral distortions (μ/y) and FIRAS/PIXIE constraints.
• Halo-model pressure profiles and predictions for y budgets and D_ℓ^{tSZ}.
• Multifrequency foreground cleaning and beam/mask propagation (pseudo-C_ℓ).
• Contributions of clusters/groups/WHIM and reionization to the y budget and their uncertainties.
• y–κ cross-correlations and energy-injection window functions for consistency tests.

Appendix A — Data Dictionary & Processing Details

• Fields & Units
  y_total, y_budget: dimensionless; D_ℓ^{tSZ}: μK²; ΔE/E: dimensionless; rho_fore: dimensionless; chi2_per_dof: dimensionless.
• Processing & Calibration
  Unified bandpasses, masks/beams/windows, and frequency weights; pseudo-C_ℓ de-mixing; GP smoothing of spectra/power; multifrequency regression to suppress CIB/dust/radio; halo+feedback priors with reionization τ_e; injections {gamma_Path_y0, eta_TBN_spec, beta_TPR_fore, epsilon_STG_y} to assess identifiability and bias.

Appendix B — Sensitivity & Robustness Checks

• Prior Sensitivity
  Posterior centres of y_total, y_budget, and D_ℓ^{tSZ} are stable under loose vs. informative priors; the eta_TBN_spec ceiling shows mild sensitivity to mask and bandpass weights without altering conclusions.
• Partition & Swap Tests
  Consistent across y-map recipes, mask complexities, cluster mass–redshift, and WHIM fractions; after train/validation swaps, BiasClosure and key parameters show no systematic drift.
• Injection–Recovery
  Near-linear recoveries for injected {epsilon_STG_y, gamma_Path_y0, eta_TBN_spec, beta_TPR_fore}; with gamma_Path_y0 = 0 injected, recovered significance is null, supporting the zero-baseline assumption.