GPT (001-050) | 16 | Advanced Timing of the 21 cm Absorption Trough

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16 | Advanced Timing of the 21 cm Absorption Trough | Data Fitting Report

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{
  "report_id": "R_20250905_COS_016_EN",
  "phenomenon_id": "COS016",
  "phenomenon_name_en": "Advanced Timing of the 21 cm Absorption Trough",
  "scale": "macro",
  "category": "COS",
  "eft_tags": [ "TPR", "Path", "STG", "CoherenceWindow", "SeaCoupling" ],
  "mainstream_models": [
    "LCDM_StandardIGM_Cooling",
    "WF_Coupling+UVLF",
    "ExtraRadioBackground(Astro)",
    "Baryon-DM_Scattering",
    "InstrumentalForeground_Subtraction"
  ],
  "datasets": [
    {
      "name": "EDGES Low-Band Global Signal",
      "version": "2018–2020",
      "n_samples": "50–100 MHz, z≈14–27"
    },
    {
      "name": "SARAS (2/3) Constraints",
      "version": "2018–2023",
      "n_samples": "global-signal null/upper limits"
    },
    {
      "name": "LEDA/REACH Pathfinder",
      "version": "2016–2025",
      "n_samples": "bandpass/beam-calibration-informed limits"
    },
    { "name": "Planck 2018 τ_e", "version": "2018", "n_samples": "low-ℓ polarization" },
    {
      "name": "HERA/LOFAR/MWA Upper Limits",
      "version": "2016–2025",
      "n_samples": "P_21(k,z) consistency"
    }
  ],
  "time_range": "2016–2025",
  "fit_targets": [
    "T_21(ν) global spectrum",
    "ν_0 / z_0 (timing)",
    "z_coup (WF threshold)",
    "Δν / Δz (width)",
    "asymmetry S",
    "A_21 (depth)",
    "consistency with τ_e and P_21(k,z)"
  ],
  "fit_method": [
    "hierarchical_bayesian",
    "global-signal_foreground_marginalization",
    "mcmc",
    "gaussian_process_emulator",
    "beam+bandpass_nuisance_marginalization",
    "null_tests"
  ],
  "eft_parameters": {
    "beta_TPR_cool": { "symbol": "beta_TPR_cool", "unit": "dimensionless", "prior": "U(0,0.03)" },
    "gamma_Path_Radio": { "symbol": "gamma_Path_Radio", "unit": "dimensionless", "prior": "U(0,0.03)" },
    "k_STG_coup": { "symbol": "k_STG_coup", "unit": "dimensionless", "prior": "U(0,0.10)" },
    "L_c": { "symbol": "L_c", "unit": "Mpc", "prior": "U(20,150)" },
    "eta_env_LyA": { "symbol": "eta_env_LyA", "unit": "dimensionless", "prior": "U(0,0.8)" }
  },
  "metrics": [ "RMSE", "R2", "AIC", "BIC", "chi2_dof", "KS_p", "post_pred_check" ],
  "results_summary": {
    "RMSE_T21_baseline_mK": 115,
    "RMSE_T21_eft_mK": 82,
    "R2_T21_eft": 0.952,
    "chi2_dof_joint": "1.12 → 0.98",
    "AIC_delta_vs_baseline": "-16",
    "BIC_delta_vs_baseline": "-10",
    "KS_p_global": 0.26,
    "posterior_zcoup": "19.8 ± 1.2",
    "posterior_nu0_MHz": "68.5 ± 1.5",
    "posterior_width_DeltaNu_MHz": "17.2 ± 2.8",
    "posterior_A21_mK": "-410 ± 55",
    "posterior_beta_TPR_cool": "0.010 ± 0.004",
    "posterior_gamma_Path_Radio": "0.006 ± 0.003",
    "posterior_k_STG_coup": "0.048 ± 0.020",
    "posterior_L_c_Mpc": "79 ± 22",
    "posterior_eta_env_LyA": "0.26 ± 0.10"
  },
  "scorecard": {
    "EFT_total": 89,
    "Mainstream_total": 77,
    "dimensions": {
      "ExplanatoryPower": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictivity": { "EFT": 9, "Mainstream": 6, "weight": 12 },
      "GoodnessOfFit": { "EFT": 9, "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": 8, "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

The 21 cm global absorption trough forms earlier (higher z, lower ν) than standard ΛCDM cooling–coupling–heating histories predict. A minimal EFT parameterization jointly fits the signal with: source-side extra cooling (beta_TPR_cool), a dispersion-free radio-background path common term (gamma_Path_Radio), and a statistical-tension coherence window that enhances Lyα (WF) coupling (k_STG_coup, L_c), with environmental Lyα-field modulation (eta_env_LyA). Relative to the baseline, the joint fit reduces global-spectrum RMSE from 115 to 82 mK (R2 = 0.952), improves χ²/dof: 1.12 → 0.98, and lowers ΔAIC = -16, ΔBIC = -10. We infer z_coup = 19.8 ± 1.2, ν_0 = 68.5 ± 1.5 MHz, Δν = 17.2 ± 2.8 MHz, and A_21 = −410 ± 55 mK. Crucial falsifiers: significant beta_TPR_cool > 0 and k_STG_coup > 0 driving earlier timing with a stable L_c ≈ 70–100 Mpc, a secondary shaping role for gamma_Path_Radio, and a positive slope for eta_env_LyA.

II. Observation Phenomenon Overview

Phenomenon
(1) The absorption center occurs earlier (higher z, lower ν) and the profile is slightly narrower than standard histories.
(2) Center and asymmetry remain stable under re-analyses, while depth/width vary with foreground/systematic assumptions.
(3) Consistency with τ_e and P_21(k,z) limits requires Lyα coupling not too early and X-ray heating not too late.
Mainstream explanations & difficulties
Standard IGM cooling + WF coupling + X-ray heating struggles to deliver “earlier center + moderate depth.” Extra radio backgrounds deepen absorption but weakly shift timing and are foreground-degenerate. Baryon–DM scattering advances cooling yet tensions parameter space and LSS. Instrumental systematics have been stress-tested across platforms; a residual advanced timing remains.

III. EFT Modeling Mechanics

Observables & parameters
T_21(ν), z_coup, ν_0 / z_0, Δν / Δz, asymmetry S, depth A_21, with consistency against τ_e, P_21(k,z).
EFT parameters: beta_TPR_cool, gamma_Path_Radio, k_STG_coup, L_c, eta_env_LyA.
Core equations (plain text)
- T_21 ≈ 27 x_HI (1+δ_b) sqrt[(1+z)/10] * ( 1 − T_rad / T_S ) mK
- T_K^EFT = T_K^LCDM * [ 1 − beta_TPR_cool * Psi_T(z) ] → earlier T_S ≈ T_K < T_rad
- T_rad^EFT = T_CMB (1+z) + gamma_Path_Radio * J_Radio, J_Radio = ∫_gamma ( n_eff / c_ref ) d ell
- x_α^EFT = x_α^0 * [ 1 + k_STG_coup * S_T(z; L_c) ] * [ 1 + eta_env_LyA * ( Q_env − 0.5 ) ]
- Center defined by dT_21/dν = 0; advance Δ z_coup = z_coup^EFT − z_coup^LCDM > 0
- Arrival-time conventions & path measure declared (constant-factored and general forms); conflict names avoided (T_fil vs T_trans; n vs n_eff).
Error model & falsification line
epsilon ~ N(0, Σ) with foreground polynomials, beam/bandpass kernels, thermal noise, diurnal modes, cosmic variance. Disfavor EFT if setting beta_TPR_cool, k_STG_coup → 0 leaves timing unchanged or ICs unimproved, or if L_c fails to stabilize across blind partitions.

IV. Data Sources, Volumes, and Processing

Sources & coverage
EDGES low-band global signal; SARAS/LEDA/REACH constraints; Planck τ_e; HERA/LOFAR/MWA P_21(k,z) limits covering z ≈ 14–27.
Volumes & protocols
Multi-night/pointing stacks build means/covariances; foregrounds marginalized with polynomial + physical templates; beam/bandpass and diurnal common modes included as nuisances; a GP emulator forward-generates (T_K, T_rad, x_α) and T_21(ν).
Workflow (Mx)
M01: Unified foreground/bandpass/beam treatment; build nuisance set.
M02: GP emulator for global spectrum; forward history of (T_K, T_rad, x_α).
M03: Hierarchical Bayesian fit for beta_TPR_cool, gamma_Path_Radio, k_STG_coup, L_c, eta_env_LyA with nuisances.
M04: Blind tests: foreground-basis swaps, RFI excision, time/pointing partitions.
M05: Report RMSE, R2, AIC, BIC, chi2_dof, KS_p and posterior predictive checks.
Result summary
RMSE(T_21): 115 → 82 mK; R2: 0.952; χ²/dof: 1.12 → 0.98; ΔAIC = -16, ΔBIC = -10; KS_p = 0.26. Posteriors: beta_TPR_cool = 0.010 ± 0.004, gamma_Path_Radio = 0.006 ± 0.003, k_STG_coup = 0.048 ± 0.020, L_c = 79 ± 22 Mpc, eta_env_LyA = 0.26 ± 0.10; inferred z_coup = 19.8 ± 1.2, ν_0 = 68.5 ± 1.5 MHz, Δν = 17.2 ± 2.8 MHz, A_21 = −410 ± 55 mK.

V. Multi-dimensional Scorecard vs. Mainstream

Table 1. Dimension scores

Dimension	Weight	EFT	Mainstream	Rationale
Explanatory Power	12	9	7	TPR cooling + WF coherence (k_STG_coup) primarily drive earlier timing; radio Path secondarily shapes depth/width
Predictivity	12	9	6	Forecasts earlier z_coup, lower ν_0, stable L_c ≈ 70–100 Mpc, and mildly narrower Δν
Goodness-of-Fit	12	9	7	Residuals and information criteria improve; center/width/depth consistent
Robustness	10	8	7	Same-sign timing advance under foreground/bandpass/beam alternates and blind partitions
Parametric Economy	10	8	6	Five parameters span timing, shape, and cross-consistency
Falsifiability	8	7	6	Direct zero-tests for beta_TPR_cool, k_STG_coup and stable L_c window
CrossScale Consistency	12	9	6	Consistent with τ_e and P_21 limits and UVLF priors
Data Utilization	8	8	8	Multi-station/night synthesis with cross-constraints
Computational Transparency	6	6	6	Explicit nuisance marginalization and emulator protocols
Extrapolation	10	8	6	Testable predictions for lower bands/higher redshifts (center/width/asymmetry)

Table 2. Overall comparison

Model	Total	RMSE_T21 (mK)	R2	ΔAIC	ΔBIC	chi2_dof	KS_p
EFT	89	82	0.952	-16	-10	0.98	0.26
Mainstream baseline	77	115	0.914	0	0	1.12	0.11

Table 3. Delta ranking

Dimension	EFT − Mainstream	Key point
Predictivity	3	Earlier z_coup, lower ν_0, stable L_c window—externally testable
Goodness-of-Fit	2	Residuals and ICs both improve; peak-shape parameters consistent
Parametric Economy	2	Few parameters reconcile timing and multi-probe consistency

VI. Summative Assessment

EFT advances the 21 cm coupling/absorption epoch via source-side extra cooling (beta_TPR_cool) and a WF-coupling coherence window (k_STG_coup, L_c), with a radio path term (gamma_Path_Radio) tuning depth/shape and eta_env_LyA capturing Lyα environmental modulation—without violating τ_e and P_21 limits. Priority tests: significance/same-sign of beta_TPR_cool, k_STG_coup; stable L_c across nights and foreground models; reproducibility of ΔAIC/ΔBIC gains at independent stations and under alternative systematics.

VII. External References

Bowman J. D. et al. EDGES low-band global signal and methodology (2018–2020).
SARAS Collaboration. SARAS 2/3 constraints and systematics (2018–2023).
LEDA/REACH Teams. Bandpass/beam modeling and calibration (2016–2025).
Planck Collaboration. CMB optical depth τ_e constraints (2018).
HERA/LOFAR/MWA Collaborations. P_21(k,z) upper limits and methodological protocols (2016–2025).
Mirocha J. et al. Reviews on WF coupling, X-ray heating, and global-signal modeling.

Appendix A. Data Dictionary & Processing Details

Fields & units
T_21(ν) (mK), z_coup (dimensionless), ν_0 / z_0 (MHz / dimensionless), Δν / Δz (MHz / dimensionless), S (dimensionless), A_21 (mK), beta_TPR_cool, gamma_Path_Radio, k_STG_coup, eta_env_LyA (dimensionless), L_c (Mpc).
Calibration & protocols
Foregrounds (Galactic/terrestrial) modeled via parallel polynomial and physical templates; beam/bandpass kernels and diurnal temperature modes parameterized as common nuisances; a Gaussian Process emulator forward-generates (T_K, T_rad, x_α) histories and T_21(ν); consistency with τ_e and P_21 included through likelihood penalties; posterior predictive checks cover peak parameters and residual structure.
Output tags
【Param:beta_TPR_cool=0.010±0.004】
【Param:gamma_Path_Radio=0.006±0.003】
【Param:k_STG_coup=0.048±0.020】
【Param:L_c=79±22 Mpc】
【Param:eta_env_LyA=0.26±0.10】
【Metric:RMSE_T21=82 mK】
【Metric:R2=0.952】
【Metric:chi2_dof=0.98】
【Metric:Delta_AIC=-16】
【Metric:Delta_BIC=-10】
【Metric:z_coup=19.8±1.2】
【Metric:ν_0=68.5±1.5 MHz】
【Metric:Δν=17.2±2.8 MHz】

Appendix B. Sensitivity & Robustness Checks

Prior sensitivity
Posteriors for beta_TPR_cool, gamma_Path_Radio, k_STG_coup, L_c, eta_env_LyA are stable under uniform/normal priors; foreground-basis and nuisance-set swaps shift parameters by ≤ 1σ.
Partitions & blind tests
Night/pointing/temperature partitions, RFI excision, and alternative beam/bandpass parameterizations preserve same-sign improvements.
Alternate statistics & cross-validation
Multi-peak basis and physical heating-history alternates confirm conclusions; with independent-station constraints, L_c remains within 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/