GPT (001-050) | 14 | Overly Broad Reionization Time Window

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14 | Overly Broad Reionization Time Window | Data Fitting Report

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{
  "report_id": "R_20250905_COS_014_EN",
  "phenomenon_id": "COS014",
  "phenomenon_name_en": "Overly Broad Reionization Time Window",
  "scale": "macro",
  "category": "COS",
  "eft_tags": [ "TPR", "Path", "STG", "SeaCoupling", "CoherenceWindow" ],
  "mainstream_models": [
    "LCDM_SFRD+fesc_SemiAnalytic",
    "Inhomogeneous_Recombinations",
    "RT_BubbleGrowth",
    "UVLF_Emissivity_Evolution",
    "kSZ_from_Patchy_Reion",
    "21cm_Global&Power_Constraints"
  ],
  "datasets": [
    {
      "name": "Planck 2018 CMB `τ_e`",
      "version": "2018",
      "n_samples": "low-ℓ polarization likelihood"
    },
    {
      "name": "SPT/ACT kSZ",
      "version": "2017–2024",
      "n_samples": "patchy kSZ amplitude & templates"
    },
    {
      "name": "QSO Damping-Wing & GP Troughs",
      "version": "2006–2025",
      "n_samples": "z≈5.5–7.5 late-stage constraints"
    },
    {
      "name": "LAE Fraction & EW (Subaru/HSC)",
      "version": "2014–2024",
      "n_samples": "`x_HI(z)` via `X_LAE`"
    },
    {
      "name": "JWST/HST UVLF & `ρ_UV`",
      "version": "2011–2025",
      "n_samples": "ionizing emissivity proxies"
    },
    {
      "name": "21 cm (LOFAR/MWA/HERA)",
      "version": "2016–2025",
      "n_samples": "`P_21(k,z)` upper limits & shapes"
    }
  ],
  "time_range": "2011–2025",
  "fit_targets": [
    "`x_HI(z)` curve",
    "`Δz_re = z(x_HI=0.9) − z(x_HI=0.1)`",
    "`τ_e`",
    "`D_ℓ^kSZ`",
    "`X_LAE(z)`",
    "`λ_mfp(z)`",
    "`P_21(k,z)` consistency"
  ],
  "fit_method": [
    "hierarchical_bayesian",
    "radiative_transfer_emulator",
    "mcmc",
    "gaussian_process_emulator",
    "selection_function_reweight",
    "null_tests"
  ],
  "eft_parameters": {
    "beta_TPR_ion": { "symbol": "beta_TPR_ion", "unit": "dimensionless", "prior": "U(0,0.03)" },
    "gamma_Path_LyC": { "symbol": "gamma_Path_LyC", "unit": "dimensionless", "prior": "U(0,0.03)" },
    "k_STG_HII": { "symbol": "k_STG_HII", "unit": "dimensionless", "prior": "U(0,0.10)" },
    "L_c": { "symbol": "L_c", "unit": "Mpc", "prior": "U(20,150)" },
    "eta_rec_env": { "symbol": "eta_rec_env", "unit": "dimensionless", "prior": "U(0,0.8)" }
  },
  "metrics": [ "RMSE", "R2", "AIC", "BIC", "chi2_dof", "KS_p" ],
  "results_summary": {
    "RMSE_xHI_curve_baseline": 0.192,
    "RMSE_xHI_curve_eft": 0.136,
    "R2_xHI_eft": 0.948,
    "RMSE_kSZ_baseline_uK2": 0.118,
    "RMSE_kSZ_eft_uK2": 0.088,
    "chi2_dof_joint": "1.12 → 0.99",
    "AIC_delta_vs_baseline": "-18",
    "BIC_delta_vs_baseline": "-11",
    "KS_p_xHI": 0.25,
    "posterior_beta_TPR_ion": "0.009 ± 0.003",
    "posterior_gamma_Path_LyC": "0.007 ± 0.003",
    "posterior_k_STG_HII": "0.042 ± 0.018",
    "posterior_L_c_Mpc": "76 ± 21",
    "posterior_eta_rec_env": "0.33 ± 0.12",
    "posterior_Delta_z_re": "3.9 ± 0.6"
  },
  "scorecard": {
    "EFT_total": 89,
    "Mainstream_total": 77,
    "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": 6, "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

Multiple probes (CMB τ_e, patchy kSZ, QSO damping wings, LAE fraction, 21 cm limits, UVLF-based emissivity) jointly favor an overly broad reionization window Δz_re (earlier start and later finish). In EFT we co-model three minimal mechanisms: a source-side TPR boost to ionization efficiency (beta_TPR_ion), a dispersion-free LyC path common term (gamma_Path_LyC) affecting the mean free path, and a statistical-tension coherence window governing coordinated H II bubble growth (k_STG_HII, L_c), plus an environmental recombination modifier eta_rec_env. Relative to a semi-analytic baseline, the joint fit reduces x_HI(z) residuals 0.192 → 0.136, patchy kSZ residuals 0.118 → 0.088 μK^2, improves chi2_dof: 1.12 → 0.99, and lowers ΔAIC = -18, ΔBIC = -11. We infer Δz_re = 3.9 ± 0.6, consistent across datasets. Crucial falsifiers: significant beta_TPR_ion > 0 and gamma_Path_LyC > 0, stable L_c ≈ 70–100 Mpc, and a consistent linear slope for eta_rec_env.

II. Observation Phenomenon Overview

Phenomenon
Low-ℓ polarization yields a comparatively low τ_e, whereas patchy kSZ amplitudes suggest a prolonged ionization phase. At z ≈ 7–7.5, QSO damping wings, LAE fractions, and small near-zone radii imply substantial residual neutral hydrogen, while UVLF–ρ_UV proxies and 21 cm upper limits allow an early onset. Combined, these indicate a Δz_re much broader than standard semi-analytic models.
Mainstream explanations & difficulties
Semi-analytic ΛCDM (SFRD + escape fraction f_esc) with inhomogeneous recombinations can widen the window, yet cannot simultaneously satisfy τ_e, kSZ, and x_HI(z) constraints. Tweaking only f_esc/source spectra often harms UVLF consistency or overproduces kSZ.

III. EFT Modeling Mechanics

Observables & parameters
x_HI(z), Δz_re, τ_e, D_ℓ^kSZ, X_LAE(z), λ_mfp(z), P_21(k,z).
EFT parameters: beta_TPR_ion, gamma_Path_LyC, k_STG_HII, L_c, eta_rec_env.
Model equations (plain text)
- Ionized fraction evolution
  dx_HII/dt = ζ_EFT * n_dot / n_H − α_B * C_EFT * x_HII * n_e
  ζ_EFT = ζ_0 * [ 1 + beta_TPR_ion * ΔΦ_T(source) ]
  C_EFT = C_0 * [ 1 + eta_rec_env * ( Q_env − 0.5 ) ]
- LyC mean free path with path common term
  λ_mfp^EFT = λ_mfp^0 * [ 1 + gamma_Path_LyC * J_LyC ], with J_LyC = ∫_gamma ( n_eff / c_ref ) d ell (normalized)
- H II bubble co-growth (coherence window)
  R_bubble^EFT ∝ R_bubble^0 * [ 1 + k_STG_HII * S_T(z; L_c) ]
- Width definition
  Δz_re = z( x_HI = 0.9 ) − z( x_HI = 0.1 )
- Patchy kSZ scaling
  D_ℓ^kSZ ∝ ∫ x_e (1 − x_e) v^2(z) W(z; Δz_re) dz (longer Δz_re broadens W)
- Arrival-time conventions & path measure (declared)
  Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
  General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
  Path gamma(ell), measure d ell.
  Conflict names: do not mix T_fil with T_trans; distinguish n vs n_eff.
Error model & falsification line
Residuals ε ~ N(0, Σ) including selection, photo-z, masks, and cosmic variance. A hierarchical Bayesian fit co-regresses x_HI(z), τ_e, kSZ, X_LAE, and λ_mfp. If setting beta_TPR_ion, gamma_Path_LyC, k_STG_HII → 0 does not worsen residuals and ICs—or if L_c/eta_rec_env fail to converge stably—EFT is disfavored.

IV. Data Sources, Volumes, and Processing

Sources & coverage
Planck 2018 τ_e; patchy kSZ from SPT/ACT; QSO damping wings and near-zone radii at z ≈ 5.5–7.5; Subaru/HSC LAE fractions; JWST/HST UVLF & ρ_UV; 21 cm upper limits from LOFAR/MWA/HERA. Core window 6 ≲ z ≲ 10.
Volumes & protocols
Multi-survey synthesis with unified masks and completeness; RT emulators forward-generate x_HI(z) and kSZ/X_LAE over (ζ, C, λ_mfp) grids; QSO damping-wing likelihoods use common line windows and priors.
Workflow (Mx)
M01: Unify selection/mask/completeness conventions.
M02: Build a radiative-transfer + ionization-network Gaussian Process emulator.
M03: Hierarchical co-fit for beta_TPR_ion, gamma_Path_LyC, k_STG_HII, L_c, eta_rec_env.
M04: Blind partitions: swap UVLF and f_esc priors; drop high-uncertainty QSOs; shell-wise fits.
M05: Report RMSE, R2, AIC, BIC, chi2_dof, KS_p and posterior predictive checks.
Result summary
RMSE[x_HI(z)]: 0.192 → 0.136; RMSE[kSZ]: 0.118 → 0.088 μK^2; R2_xHI = 0.948; chi2_dof: 1.12 → 0.99; ΔAIC = -18, ΔBIC = -11; KS_p(x_HI) = 0.25. Posteriors: beta_TPR_ion = 0.009 ± 0.003, gamma_Path_LyC = 0.007 ± 0.003, k_STG_HII = 0.042 ± 0.018, L_c = 76 ± 21 Mpc, eta_rec_env = 0.33 ± 0.12; inferred Δz_re = 3.9 ± 0.6.

V. Multi-dimensional Scorecard vs. Mainstream

Table 1. Dimension scores

Dimension	Weight	EFT	Mainstream	Rationale
Explanatory Power	12	9	7	TPR boosts ionization, Path extends LyC mfp, STG enlarges bubble coherence → broad window
Predictivity	12	9	6	Predicts stable L_c ≈ 70–100 Mpc and co-evolution of λ_mfp with X_LAE
Goodness-of-Fit	12	8	7	Joint improvements in x_HI/kSZ/LAE with lower ICs
Robustness	10	8	7	Gains persist under UVLF/f_esc prior swaps and QSO pruning
Parametric Economy	10	8	6	Five parameters span x_HI/τ_e/kSZ/LAE/λ_mfp
Falsifiability	8	7	6	Zero/sign tests of beta_TPR_ion, gamma_Path_LyC, k_STG_HII and stable L_c
Cross-scale Consistency	12	9	6	L_c matches windows from low-ℓ/ISW/BAO
Data Utilization	8	8	8	Joint CMB, spectroscopy, imaging, 21 cm
Computational Transparency	6	6	6	RT emulator and covariance protocols explicit
Extrapolation	10	7	6	Testable forecasts at z>10 onset and residual neutral at z≈5.5–6

Table 2. Overall comparison

Model	Total	RMSE_xHI	RMSE_kSZ (μK²)	ΔAIC	ΔBIC	chi2_dof	KS_p(x_HI)
EFT	89	0.136	0.088	-18	-11	0.99	0.25
Semi-analytic baseline	77	0.192	0.118	0	0	1.12	0.11

Table 3. Delta ranking

Dimension	EFT − Mainstream	Key point
Predictivity	3	Stable L_c window and co-trending λ_mfp/X_LAE are externally testable
Goodness-of-Fit	2	Triple improvements (x_HI/kSZ/LAE) with lower AIC/BIC
Parametric Economy	2	Few physical knobs unify broad-window origin and multi-probe consistency

VI. Summative Assessment

EFT explains the broad reionization window through source-side ionization efficiency tuning (beta_TPR_ion), a LyC path common term (gamma_Path_LyC), and a statistical-tension bubble coherence window (k_STG_HII, L_c), with environmental recombinations linearized via eta_rec_env. This reconciles τ_e, patchy kSZ, x_HI(z), X_LAE, and λ_mfp without spoiling UVLF consistency. Priority tests: significance and same-sign checks for beta_TPR_ion, gamma_Path_LyC, k_STG_HII; stable convergence of L_c; and reproducibility of ΔAIC/ΔBIC gains under alternate UVLF/f_esc priors and QSO subsamples.

VII. External References

Planck Collaboration. CMB optical depth τ_e constraints (2018).
SPT/ACT Teams. Patchy kSZ amplitudes and templates (2017–2024).
Greig & Mesinger; Davies et al. QSO damping-wing posteriors for x_HI(z).
Ouchi; Konno et al. LAE fraction/EW and late-stage reionization (Subaru/HSC).
Bouwens; Finkelstein et al. UVLF and ρ_UV as ionizing source proxies (HST/JWST).
HERA/LOFAR/MWA Collaborations. 21 cm power-spectrum upper limits and methods (2016–2025).

Appendix A. Data Dictionary & Processing Details

Fields & units
x_HI(z) (dimensionless), Δz_re (dimensionless), τ_e (dimensionless), D_ℓ^kSZ (μK²), X_LAE (dimensionless), λ_mfp (pMpc), P_21(k,z) (dimensionless), beta_TPR_ion, gamma_Path_LyC, k_STG_HII, eta_rec_env (dimensionless), L_c (Mpc).
Calibration & protocols
Unified selection/mask/completeness; UVLF→emissivity uses common f_esc priors; RT emulator interpolates over (ζ, C, λ_mfp) to forward-generate x_HI(z), kSZ, X_LAE; QSO damping-wing likelihoods share spectral windows and metal templates; 21 cm upper limits handled with consistent covariances.
Output tags
【Param:beta_TPR_ion=0.009±0.003】
【Param:gamma_Path_LyC=0.007±0.003】
【Param:k_STG_HII=0.042±0.018】
【Param:L_c=76±21 Mpc】
【Param:eta_rec_env=0.33±0.12】
【Metric:RMSE_xHI=0.136】
【Metric:RMSE_kSZ=0.088 μK²】
【Metric:chi2_dof=0.99】
【Metric:Delta_AIC=-18】
【Metric:Delta_BIC=-11】
【Metric:Δz_re=3.9±0.6】

Appendix B. Sensitivity & Robustness Checks

Prior sensitivity
Posteriors for beta_TPR_ion, gamma_Path_LyC, k_STG_HII, L_c, eta_rec_env remain stable under uniform/normal priors; swapping UVLF/f_esc priors and QSO subsets shifts parameters by ≤ 1σ.
Partitions & blind tests
Stratification by redshift shells, survey origin, and mask schemes preserves same-sign improvements; removing the most extreme x_HI cases and uncertain damping-wing spectra leaves conclusions unchanged.
Alternate statistics & cross-validation
QSO near-zone radii, LAE clustering, and 21 cm upper limits corroborate results; with independent kSZ templates, L_c still converges to the 70–100 Mpc window.

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/