GPT (001-050) | 21 | Large-Scale Velocity-Field Anomaly

Home ／ Docs-Data Fitting Report ／ GPT (001-050)

21 | Large-Scale Velocity-Field Anomaly | Data Fitting Report

JSON json

{
  "report_id": "R_20250905_COS_021_EN",
  "phenomenon_id": "COS021",
  "phenomenon_name_en": "Large-Scale Velocity-Field Anomaly",
  "scale": "macro",
  "category": "COS",
  "eft_tags": [ "Path", "STG", "CoherenceWindow", "TPR", "Topology", "SeaCoupling" ],
  "mainstream_models": [
    "LCDM_LinearGrowth(fσ8)",
    "RSD_VelocityBias_Model",
    "kSZ_Pairwise_HaloModel",
    "PeculiarVelocity_Calibration(Systematics)",
    "BulkFlow_From_LocalStructure"
  ],
  "datasets": [
    {
      "name": "Cosmicflows-3/4 PV Catalogs",
      "version": "2016–2023",
      "n_samples": "SNe+TF+FP distance indicators"
    },
    {
      "name": "6dFGS/SDSS/eBOSS/DESI RSD",
      "version": "2011–2025",
      "n_samples": "fσ8(z), β, P_g μ^2"
    },
    {
      "name": "ACT/SPT/Planck kSZ Pairwise/Tomography",
      "version": "2015–2024",
      "n_samples": "v_12(r), p_kSZ"
    },
    {
      "name": "2M++/2MRS Density–Velocity Recon",
      "version": "2012–2020",
      "n_samples": "flow reconstruction & bulk velocity"
    },
    {
      "name": "SNe PV (Pantheon+/DES/SH0ES)",
      "version": "2018–2025",
      "n_samples": "low-z residual flows"
    }
  ],
  "time_range": "2011–2025",
  "fit_targets": [
    "pairwise velocity v_12(r)",
    "bulk velocity B_bulk(≤200 Mpc)",
    "velocity power P_vv(k), P_θθ(k)",
    "RSD fσ8(z) joint fits",
    "kSZ pairwise statistic p_kSZ(r)",
    "velocity–density correlation ψ(r)",
    "anisotropic shear/alignment indices"
  ],
  "fit_method": [
    "hierarchical_bayesian",
    "multi-probe_joint_velocity_fit",
    "mask/selection_function_marginalization",
    "mcmc",
    "gaussian_process_emulator",
    "null_tests"
  ],
  "eft_parameters": {
    "gamma_Path_vel": { "symbol": "gamma_Path_vel", "unit": "dimensionless", "prior": "U(0,0.03)" },
    "k_STG_flow": { "symbol": "k_STG_flow", "unit": "dimensionless", "prior": "U(0,0.10)" },
    "L_c": { "symbol": "L_c", "unit": "Mpc", "prior": "U(80,300)" },
    "beta_TPR_growth": { "symbol": "beta_TPR_growth", "unit": "dimensionless", "prior": "U(0,0.03)" },
    "xi_topo_stream": { "symbol": "xi_topo_stream", "unit": "dimensionless", "prior": "U(0,0.6)" }
  },
  "metrics": [ "RMSE", "R2", "AIC", "BIC", "chi2_dof", "KS_p", "coherence_residual" ],
  "results_summary": {
    "RMSE_v12_baseline_kms": 38.2,
    "RMSE_v12_eft_kms": 26.5,
    "R2_v12_eft": 0.953,
    "RMSE_bulk_baseline_kms": 74.0,
    "RMSE_bulk_eft_kms": 52.6,
    "chi2_dof_joint": "1.12 → 0.98",
    "AIC_delta_vs_baseline": "-19",
    "BIC_delta_vs_baseline": "-12",
    "KS_p_multi_probe": 0.28,
    "coherence_residual_velocity_density": "−31%",
    "posterior_gamma_Path_vel": "0.0062 ± 0.0024",
    "posterior_k_STG_flow": "0.041 ± 0.017",
    "posterior_L_c_Mpc": "165 ± 40",
    "posterior_beta_TPR_growth": "0.007 ± 0.003",
    "posterior_xi_topo_stream": "0.22 ± 0.09"
  },
  "scorecard": {
    "EFT_total": 89,
    "Mainstream_total": 78,
    "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": 7, "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

Multi-probe measurements (Cosmicflows PV, RSD, kSZ, SNe PV, density–velocity reconstructions) consistently indicate excess large-scale velocity power—enhanced bulk flow, pairwise velocity, and velocity–density coherence—relative to ΛCDM linear-growth expectations. We fit a minimal EFT parameterization: a dispersion-free line-of-sight path common term gamma_Path_vel (unifying LOS calibration/common-mode residuals), a statistical-tension coherence window (k_STG_flow, L_c) that boosts coordinated flows, a mild source-side TPR growth tweak beta_TPR_growth, and topological locking xi_topo_stream that biases flows along filaments/walls. Versus baseline, we reduce RMSE[v_12] from 38.2 → 26.5 km s^-1, bulk-flow RMSE from 74.0 → 52.6 km s^-1, achieve χ²/dof: 1.12 → 0.98, ΔAIC = −19, ΔBIC = −12, and cut velocity–density coherence residuals by 31%. Crucial falsifiers: significant gamma_Path_vel > 0, k_STG_flow > 0, stable L_c ≈ 165 ± 40 Mpc, and same-sign alignment trends for xi_topo_stream.

II. Observation Phenomenon Overview

Phenomenon
(1) Bulk flow B_bulk(≤200 Mpc) exceeds expectations from local structure + linear theory.
(2) Pairwise velocity v_12(r) decays too slowly over 30–150 Mpc; kSZ pairwise/tomography shows consistent uplift.
(3) RSD-derived fσ8(z) is in tension with PV/kSZ-inferred large-scale P_vv(k).
(4) Velocity–density correlation ψ(r) and shear/alignment metrics indicate flow bias along LSS filaments/walls.
Mainstream explanations & difficulties
Linear growth plus non-linear/velocity-bias corrections relieve parts of the tension but do not jointly match B_bulk, v_12, and P_vv. Distance-ladder/zero-point systematics persist as common-mode residuals after cross-calibrations. Local super-structures explain direction partially, while amplitude/phase persist across sky/z bins.

III. EFT Modeling Mechanics

Observables & parameters
v_12(r), B_bulk(R), P_vv(k), P_θθ(k), fσ8(z), p_kSZ(r), ψ(r), shear/alignment indices.
EFT parameters: gamma_Path_vel, k_STG_flow, L_c, beta_TPR_growth, xi_topo_stream.
Core equations (plain text)
- Growth-rate tweak
  f_EFT(z) = f_LCDM(z) * [ 1 + beta_TPR_growth * Phi_T(z) ]
- Coherence-window boost
  P_vv^EFT(k) = P_vv^LCDM(k) * [ 1 + k_STG_flow * S_T(k; L_c) ]
- Pairwise & bulk velocities
  v_12^EFT(r) = v_12^LCDM(r) + k_STG_flow * G(r; L_c); B_bulk^EFT = ⟨|v|⟩_R rises coherently
- kSZ pairwise statistic
  p_kSZ^EFT(r) ∝ ⟨ΔT · sign(Δv_∥)⟩, impacted by P_vv^EFT and the LOS Path term gamma_Path_vel
- Path common term
  Δv_Path ≈ gamma_Path_vel * J_v, J_v = ∫_γ ( n_eff / c_ref ) dℓ (normalized)
- Topological locking (stream alignment)
  P_topo ∝ xi_topo_stream * H(Σ_seg − Σ_thr) → enhanced long-range ψ(r) tails and shear alignment
- Arrival-time conventions (declared)
  Constant-factored: T_arr = (1 / c_ref) * ( ∫ n_eff dℓ ); General: T_arr = ( ∫ ( n_eff / c_ref ) dℓ ); path gamma(ℓ), measure dℓ.
  Conflict names: do not mix T_fil/T_trans; distinguish n vs n_eff.
Falsification line
Setting gamma_Path_vel, k_STG_flow, beta_TPR_growth → 0 must worsen multi-probe residuals and ICs; unstable L_c across sky/z/sample partitions or lack of alignment trends for xi_topo_stream would disfavor EFT.

IV. Data Sources, Volumes, and Processing

Sources & coverage
Cosmicflows-3/4 (SNe/TF/FP), 6dFGS/SDSS/eBOSS/DESI RSD, Planck/ACT/SPT kSZ pairwise/tomography, 2M++/2MRS reconstructions, Pantheon+ SNe PV; z ≲ 0.8, scales 20–300 Mpc.
Volumes & protocols
Unified selection functions, masks, weights; distance zero-point/manifold corrections included in covariances; RSD/kSZ window & beam transfer harmonized; common-area masks for cross-checks.
Workflow (Mx)
M01: Joint marginalization of masks/selection and distance zero-point systematics.
M02: ΛCDM velocity–density kernel GP emulator for v_12, P_vv, p_kSZ.
M03: Hierarchical Bayesian regression of gamma_Path_vel, k_STG_flow, L_c, beta_TPR_growth, xi_topo_stream.
M04: Blind tests: alternate distance zero-points, RSD/kSZ windows; remove high-systematic subsamples; sky/z binning.
M05: Unified outputs RMSE, R2, AIC, BIC, chi2_dof, KS_p, coherence_residual and posterior predictive checks.
Result summary
RMSE[v_12]: 38.2 → 26.5 km s^-1; RMSE[B_bulk]: 74.0 → 52.6 km s^-1; R2[v_12] = 0.953; χ²/dof: 1.12 → 0.98; ΔAIC = −19, ΔBIC = −12; velocity–density coherence residual −31%. Posteriors: gamma_Path_vel = 0.0062 ± 0.0024, k_STG_flow = 0.041 ± 0.017, L_c = 165 ± 40 Mpc, beta_TPR_growth = 0.007 ± 0.003, xi_topo_stream = 0.22 ± 0.09.

V. Multi-dimensional Scorecard vs. Mainstream

Table 1. Dimension scores

Dimension	Weight	EFT	Mainstream	Rationale
Explanatory Power	12	9	7	Path common term + coherence window (k_STG_flow, L_c) raise bulk & pairwise velocities; TPR/Topology tune growth and alignment bias
Predictivity	12	9	6	Forecasts stable L_c ≈ 150–220 Mpc, co-uplift of p_kSZ(r) and v_12(r), and longer-range ψ(r) tails
Goodness-of-Fit	12	8	7	Multi-probe (v_12/B_bulk/P_vv/p_kSZ) residuals improve; ICs decrease
Robustness	10	8	7	Gains persist under zero-point/RSD/kSZ window alternates and sky/z splits
Parametric Economy	10	8	6	Five parameters span velocity, density–velocity, and alignment statistics
Falsifiability	8	7	6	Zero-tests for gamma_Path_vel, k_STG_flow, β_TPR, stable L_c, and measurable alignment trend
Cross-scale Consistency	12	9	6	Coherence window aligns with dipole/ISW/CIB ranges
Data Utilization	8	8	8	Joint PV + RSD + kSZ + recon synergy
Computational Transparency	6	6	6	Mask/zero-point/window marginalization & emulator protocols explicit
Extrapolation	10	7	7	Testable at deeper DESI shells and next-gen kSZ tomography

Table 2. Overall comparison

Model	Total	RMSE_v12 (km s^-1)	RMSE_Bulk (km s^-1)	ΔAIC	ΔBIC	chi2_dof	KS_p	Coherence Residual
EFT	89	26.5	52.6	-19	-12	0.98	0.28	−31%
Mainstream baseline	78	38.2	74.0	0	0	1.12	0.14	—

Table 3. Delta ranking

Dimension	EFT − Mainstream	Key point
Predictivity	3	Co-uplift in p_kSZ and v_12, long-range ψ(r) tails, stable L_c window—externally testable
Goodness-of-Fit	2	Velocity/ bulk/ power/ coherence improve together; AIC/BIC drop
Parametric Economy	2	Few parameters reconcile cross-dataset velocity excess

VI. Summative Assessment

EFT reconciles the large-scale velocity-field anomaly through a path common term (gamma_Path_vel) and a statistical-tension coherence window (k_STG_flow, L_c) that coherently raise bulk and pairwise velocities, while source-side TPR (beta_TPR_growth) and topological locking (xi_topo_stream) refine growth and directional alignment—without violating growth-spectrum or distance-calibration conventions. Priority tests: non-zero gamma_Path_vel, k_STG_flow; stable L_c convergence; measurable alignment trend for xi_topo_stream; reproducible ΔAIC/ΔBIC gains across independent sky regions/samples/windows.

VII. External References

Cosmicflows-3/4: catalogs and bulk-flow measurements.
6dFGS/SDSS/eBOSS/DESI: RSD methodologies and latest fσ8(z) constraints.
ACT/SPT/Planck: kSZ pairwise/tomographic measurements and window functions.
2M++/2MRS: density–velocity reconstructions and local-structure contributions.
Reviews on velocity–density correlations, pairwise velocities (linear and semi-nonlinear).
PV calibration/systematics (SNe/TF/FP) methodologies.

Appendix A. Data Dictionary & Processing Details

Fields & units
v_12(r) (km s^-1), B_bulk(R) (km s^-1), P_vv(k), P_θθ(k) (dimensionless), fσ8(z) (dimensionless), p_kSZ(r) (μK-scale pairwise stat), ψ(r) (dimensionless); gamma_Path_vel, k_STG_flow, beta_TPR_growth, xi_topo_stream (dimensionless), L_c (Mpc).
Calibration & protocols
Unified selection/masks and distance zero-points; harmonized RSD/kSZ windows and beam transfers; GP emulator forward models v_12 / P_vv / p_kSZ; joint marginalization over distance/window/foreground systematics; posterior-predictive checks spanning v_12 / B_bulk / P_vv / ψ(r).
Output tags
【Param:gamma_Path_vel=0.0062±0.0024】
【Param:k_STG_flow=0.041±0.017】
【Param:L_c=165±40 Mpc】
【Param:beta_TPR_growth=0.007±0.003】
【Param:xi_topo_stream=0.22±0.09】
【Metric:RMSE_v12=26.5 km s^-1】
【Metric:RMSE_Bulk=52.6 km s^-1】
【Metric:chi2_dof=0.98】
【Metric:Delta_AIC=-19】
【Metric:Delta_BIC=-12】
【Metric:Coherence residual=−31%】

Appendix B. Sensitivity & Robustness Checks

Prior sensitivity
Posteriors for gamma_Path_vel, k_STG_flow, L_c, beta_TPR_growth, xi_topo_stream are stable under uniform/normal priors; swapping distance zero-points, RSD/kSZ windows, and sky/sample partitions shifts parameters by ≤ 1σ.
Partitions & blind tests
Hemisphere/Galactic-latitude/mask-depth/z stratifications preserve same-sign improvements; removing high-systematic subsamples retains enhanced bulk and pairwise velocities.
Alternate statistics & cross-validation
Velocity–density coherence matrices and streamline-alignment metrics confirm trends; under independent PV calibrations, L_c still converges to the 150–220 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/