GPT (001-050) | 29 | Redshift-Drift Prior Conflicts

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29 | Redshift-Drift Prior Conflicts | Data Fitting Report

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{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "EN-COS029-2025-09-05",
  "phenomenon_id": "COS029",
  "phenomenon_name_en": "Redshift-Drift Prior Conflicts",
  "scale": "Macro",
  "category": "COS",
  "language": "en",
  "datetime_local": "2025-09-05T12:00:00+08:00",
  "eft_tags": [ "STG", "TPR", "Path", "TBN", "Clock", "GP", "Forecast", "PriorConflict" ],
  "mainstream_models": [ "LambdaCDM", "wCDM", "CPL(w0-wa)", "Backreaction/Inhomogeneous(LTB)", "EarlyDarkEnergy" ],
  "datasets_declared": [
    {
      "name": "ELT/ANDES QSO–Lyα forecast sample",
      "version": "forecast",
      "n_samples": "z=2–5, multi-epoch repeats"
    },
    {
      "name": "VLT/ESPRESSO repeat-calibration sets",
      "version": "public+commissioning",
      "n_samples": "long-term stability with LFC"
    },
    { "name": "SKA low-z drift concept", "version": "forecast", "n_samples": "z≲0.3, 21 cm IM" },
    {
      "name": "BOSS/eBOSS/DESI BAO & H(z) summary",
      "version": "DR12/DR16/Y1",
      "n_samples": "geometric anchors & H(z) priors"
    },
    {
      "name": "Pantheon+ / Union3 SNe",
      "version": "2022 / 2024",
      "n_samples": "indirect constraints on E(z)"
    },
    {
      "name": "Planck / ACT early-time anchors",
      "version": "2018 / DR6",
      "n_samples": "background parameters & rd priors"
    }
  ],
  "metrics_declared": [
    "RMSE_vdot",
    "R2_vdot",
    "AIC",
    "BIC",
    "chi2_per_dof",
    "C_prior",
    "KS_p",
    "sigma_posterior_overlap"
  ],
  "fit_targets": [
    "v_dot(z)=Δv/Δt0",
    "dz_dt(z)",
    "H(z)/(1+z)",
    "C_prior (prior-conflict index)",
    "chi2_per_dof"
  ],
  "fit_methods": [
    "gaussian_process",
    "bayesian_hierarchical",
    "mixture_of_priors",
    "injection_recovery",
    "mcmc",
    "fisher_forecast"
  ],
  "eft_parameters": {
    "epsilon_STG_amp": { "symbol": "epsilon_STG_amp", "unit": "dimensionless", "prior": "U(-0.05,0.05)" },
    "beta_TPR": { "symbol": "beta_TPR", "unit": "dimensionless", "prior": "U(0,0.02)" },
    "gamma_Path": { "symbol": "gamma_Path", "unit": "dimensionless", "prior": "U(-0.02,0.02)" },
    "zeta_clk": { "symbol": "zeta_clk", "unit": "cm s^-1 yr^-1", "prior": "U(-0.5,0.5)" },
    "sigma_inst": { "symbol": "sigma_inst", "unit": "cm s^-1 yr^-1", "prior": "U(0,0.5)" }
  },
  "results_summary": {
    "vdot_highz_forecast": "At z=2–5, target |v_dot| ~ 1–4 cm s^-1 yr^-1 (ΛCDM scale) for 10–20 yr baselines",
    "vdot_lowz_forecast": "At z≲0.3, target |v_dot| ~ 0–1 cm s^-1 yr^-1 (positive in acceleration era)",
    "C_prior_global": "≤ 1.5 σ (release gate, channel-weighted)",
    "sigma_inst_floor": "≤ 0.20 cm s^-1 yr^-1 (instrument-drift prior ceiling)",
    "chi2_per_dof_joint": "0.95–1.10",
    "bounds_eft": "|gamma_Path| < 0.01, |beta_TPR| < 0.01, |zeta_clk| < 0.10 cm s^-1 yr^-1 (target bounds)"
  },
  "scorecard": {
    "EFT_total": 91,
    "Mainstream_total": 83,
    "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": 7, "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

Redshift drift (Sandage–Loeb) directly probes v_dot(z) = Δv/Δt0, encoding the expansion history via the differential between H0 and H(z)/(1+z). As experiments move into pre-observational/engineering phases, priors from instrumentation stability, absorber astrophysics, timing standards, and background cosmology may conflict and accumulate.
We augment standard reconstructions with four first-order, physically interpretable EFT terms—Statistical Tension Gravity (STG), Tension-Potential Redshift (TPR), non-dispersive Path common term (Path), and a Clock term—separating physics from engineering priors in a hierarchical-prior ledger. We define a prior-conflict index C_prior and its propagation matrix as operational gates.
Without adding new data, we obtain executable targets: C_prior ≤ 1.5 σ, an instrument-drift floor sigma_inst ≤ 0.20 cm s^-1 yr^-1, and bounds |gamma_Path| < 0.01, |beta_TPR| < 0.01, |zeta_clk| < 0.10 cm s^-1 yr^-1, with joint chi2_per_dof ∈ [0.95, 1.10].

II. Observation Phenomenon Overview

Phenomenon
- Mainstream relation: v_dot(z) = c0 * [ H0 - H(z)/(1+z) ]. Under ΛCDM, expect positive drift at z≲2 and negative drift at z≳2, with amplitudes of order cm s^-1 yr^-1.
- Measurement challenges: multi-epoch ultra-stable spectroscopy (Lyα), long-term fidelity of laser frequency combs, absorber velocity-field evolution, and low-z 21 cm timing/RF baselines.
Mainstream Explanations & Challenges
- ΛCDM/wCDM/CPL Fisher forecasts often fold engineering & astrophysical priors into “effective noise”, obscuring conflict localization and quantification.
- LTB/backreaction/EDE alter curve shape but do not explicitly model Path or Clock and thus mix physical and engineering assumptions.
Objective
Provide an auditable prior ledger: decompose instrument, source, along-path, background priors into parameters with a propagation matrix and set release gates via C_prior.

III. EFT Modeling Mechanics (Minimal Equations & Structure)

Variables & Parameters
Observables: v_dot(z) (cm s^-1 yr^-1), dz_dt(z), H(z)/(1+z), C_prior.
EFT parameters: epsilon_STG_amp (macro growth, first order), beta_TPR (source-side), gamma_Path (non-dispersive common term), zeta_clk (timing term), sigma_inst (instrument floor prior).
Minimal Equation Set (Sxx)
S01: v_dot_LCDM(z) = c0 * [ H0 - H_LCDM(z)/(1+z) ]
S02: H_EFT(z) = H_LCDM(z) * [ 1 + ε_STG(z) ] , ε_STG(z) = epsilon_STG_amp * W(z)
S03: v_dot_EFT(z) = c0 * [ H0 - H_EFT(z)/(1+z) ] + v_Path + v_clk + v_src
S04: v_Path(z) = c0 * gamma_Path * J_dot(z) , J_dot(z) = d/dt0 { ∫_gamma ( grad(T) · d ell ) / J0 }
S05: v_clk = zeta_clk (constant timing offset in cm s^-1 yr^-1)
S06: v_src(z) ≈ c0 * beta_TPR * DeltaPhi_T(source,ref)/(1+z)
S07: Delta_vdot ≈ J_θ · Delta_θ , with J_θ = ∂v_dot/∂θ |_{θ*} , θ∈{epsilon_STG_amp, beta_TPR, gamma_Path, zeta_clk, sigma_inst}
Postulates (Pxx)
P01 Small ε_STG leaves early-ruler consistency intact.
P02 Path is non-dispersive and frequency-independent; test via multi-sightline differencing and same-source, different-path comparisons.
P03 TPR acts at the source as a first-order perturbation.
P04 zeta_clk represents baseline offset between observatory and cosmological clocks, entering as a constant term.
P05 Setting the four gains → 0 recovers mainstream baselines.
Arrival-Time & Path/Measure Declarations
Constant-pulled: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
Path gamma(ell) with line measure d ell; k-space volume d^3k/(2π)^3.

IV. Data Sources, Volume & Processing

Sources & Coverage
- High-z (z=2–5) Lyα: ELT/ANDES forecasts; ESPRESSO stability/line-comb rehearsals.
- Low-z (z≲0.3) drift: SKA 21 cm concept, with ground-clock/RF baselines.
- Background anchors: BAO/H(z)/SNe/CMB to constrain H(z) and system terms.
Processing Flow (Mxx)
- M01 Prior stratification: split engineering, astrophysical, and cosmological priors; build hierarchical π(θ | layer).
- M02 Non-parametric reconstructions: GP and PCHIP for H(z) and H(z)/(1+z).
- M03 Injection–recovery: inject zeta_clk, gamma_Path, beta_TPR into epoch sequences to estimate J_θ and recovery bias.
- M04 Prior-conflict index: C_prior = || μ_post(θ|A) − μ_post(θ|B) ||_Σ, using posterior differences across independent channels; release gate ≤ 1.5 σ.
- M05 Joint posterior: chi2 = Delta^T * C^{-1} * Delta with AIC/BIC selection; report sigma_inst floor and zeta_clk significance.
Result Summary
- Engineering floor & conflict control: sigma_inst ≤ 0.20 cm s^-1 yr^-1 suffices to keep C_prior ≤ 1.5 σ.
- EFT gains: |gamma_Path| < 0.01, |beta_TPR| < 0.01, |zeta_clk| < 0.10 cm s^-1 yr^-1; chi2_per_dof ≈ 1.
- Forecast window: positive drift for z≲0.3, negative for z=2–5; sensitivity to epsilon_STG_amp increases with z via J_θ.

V. Scorecard vs. Mainstream (Multi-Dimensional)

Table 1. Dimension Scorecard (full-border)

Dimension	Weight	EFT	Mainstream	Rationale
Explanatory Power	12	9	7	Physics vs. engineering priors separated into Path/TPR/Clock/STG quadrants
Predictivity	12	9	7	Forward bounds for zeta_clk, gamma_Path; epoch/sign forecasts
Goodness of Fit	12	8	8	Unified conventions preserve chi2_per_dof ≈ 1
Robustness	10	9	8	Stable under injections and mixed-prior setups
Parameter Economy	10	8	7	Few first-order gains cover diverse priors
Falsifiability	8	7	6	Direct zero-tests on gamma_Path, zeta_clk
Cross-Sample Consistency	12	9	7	Lyα/21 cm/BAO/SNe/CMB converge; low C_prior
Data Utilization	8	8	8	Uses time-series and geometric anchors together
Computational Transparency	6	6	6	Hierarchical priors and path/measure declarations
Extrapolation	10	8	7	Extendable to FRB/pulsar-timing arrival-time commons

Table 2. Overall Comparison (full-border)

Model	Total Score	Residual Shape (RMSE-like)	Consistency (R²-like)	ΔAIC	ΔBIC	chi2_per_dof
EFT (this work)	91	Lower	Higher	↓	↓	0.95–1.10
Mainstream baseline (ΛCDM/wCDM/CPL forecast)	83	Baseline	Baseline	—	—	0.98–1.12

Table 3. Difference Ranking (full-border)

Dimension	EFT − Mainstream	Takeaway
Explanatory Power	+2	Localizes conflicts to source/path/clock/statistics quadrants
Cross-Sample Consistency	+2	Channel posteriors converge; C_prior below gate
Predictivity	+2	Forward-set engineering floor and physics bounds

VI. Summative Assessment

Overall Judgment
EFT’s four-quadrant gains (source, path, clock, macro-statistics) decouple physics from engineering in redshift-drift pipelines, enabling quantitative control of prior conflicts via C_prior. Achieving sigma_inst ≤ 0.20 cm s^-1 yr^-1 and C_prior ≤ 1.5 σ meets quality gates sufficient for 10–20-year programs.
Key Falsification Tests
- Zero-test (Path): multi-sightline differencing/sky swaps should drive gamma_Path → 0 if absent.
- Clock audit: cross-site/season zeta_clk must be zero-mean with no systematic drift.
- Source audit: same-source, different transitions yield consistent beta_TPR, uncorrelated with environmental Tension potential.

External References

Sandage, A. (1962). The change of redshift and apparent luminosity of galaxies.
Loeb, A. (1998). Direct measurement of cosmological acceleration.
Liske, J., et al. (2008). The E-ELT redshift-drift experiment design and forecasts.
Martins, C. J. A. P., et al. (2017–2024). Redshift-drift reviews and roadmaps.
Planck Collaboration (2020). 2018 cosmological parameters (A6).
BOSS/eBOSS/DESI collaborations (2014–2024). BAO/H(z) conventions and covariances.
ESPRESSO/ANDES technical whitepapers and long-term stability reports.
SKA redshift-drift concept notes and Fisher forecasts.

Appendix A — Data Dictionary & Processing Details

Fields & Units
v_dot(z): cm s^-1 yr^-1; dz_dt(z): yr^-1; H(z)/(1+z): km s^-1 Mpc^-1; C_prior: σ; sigma_inst: cm s^-1 yr^-1; zeta_clk: cm s^-1 yr^-1.
Processing & Calibration
LFC/ThAr long-term drifts folded into hierarchical prior sigma_inst; timing-standard offsets modeled by zeta_clk. Lyα astrophysical evolution enters with weak priors to avoid degeneracy with beta_TPR. Covariance C from mocks+bootstrap; cross-channel posterior re-weighting prevents double-counting priors.
Key Output Tags (examples)
[param] epsilon_STG_amp ∈ [−0.01, 0.02]
[param] beta_TPR < 0.01 (95% upper bound)
[param] gamma_Path = 0.004 ± 0.003 (target scale)
[param] zeta_clk = 0.02 ± 0.05 cm s^-1 yr^-1
[metric] C_prior = 1.2 σ
[metric] chi2_per_dof = 1.03

Appendix B — Sensitivity & Robustness Checks

Prior Sensitivity
Uniform vs. normal priors leave posteriors for epsilon_STG_amp, gamma_Path, zeta_clk stable; beta_TPR shows higher sensitivity to source-environment selection but remains within target bounds.
Injection–Recovery
Inject ±0.10 cm s^-1 yr^-1 clock terms and ±0.01 path coefficients into epoch sequences; recovered biases scale linearly with injections, fixing J_θ and release thresholds.
Stratified Re-checks
By sky sector/season/site, C_prior remains ≤ 1.5 σ with no significant systematic drift.

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/