Author: Matthew Lukin Smawfield
Version: v0.6 (Kingston upon Hull)
Date: First published: 11 January 2026 · Last updated: 29 April 2026
Status: Preprint (Open for Collaboration)
DOI: 10.5281/zenodo.18209702
Website: https://mlsmawfield.com/tep/h0/
Paper Series: TEP Series: Paper 11 (Cosmological Observations)
The Hubble Tension—the persistent 5σ discrepancy between local distance-ladder measurements (H₀ ≈ 73 km/s/Mpc) and early-universe CMB inference (H₀ = 67.4 ± 0.5 km/s/Mpc)—represents a significant challenge in precision cosmology. This study proposes that the tension arises from a systematic, environment-dependent bias in Cepheid-based distances, as predicted by the Temporal Equivalence Principle (TEP).
This study tests the hypothesis that the discrepancy arises from a violation of the isochrony axiom—the assumption that proper time accumulation is independent of the local gravitational environment. Under scalar-tensor theories that break the Strong Equivalence Principle (such as TEP), Cepheid variable stars act as environment-dependent "standard clocks." In deep gravitational potentials (high velocity dispersion σ) and active-shear environments, enhanced scalar field activity is predicted to induce period contraction relative to calibration environments. When interpreted through a universal Period-Luminosity relation, this clock-rate anomaly would mimic diminished luminosity, leading to underestimated distances and an inflated local Hubble constant.
Analysis of the SH0ES Cepheid sample (N=29), stratified by host galaxy velocity dispersion (a TEP-independent kinematic observable), reveals a statistically significant correlation between host potential depth and derived H₀ (Spearman ρ = 0.511, p = 0.0046; Pearson r = 0.462, p = 0.0116). A median-split stratification at σ_med ≈ 90 km/s yields H₀ = 67.82 ± 1.62 km/s/Mpc (low-σ; N=15) versus 72.45 ± 2.32 km/s/Mpc (high-σ; N=14), implying ΔH₀ = 4.63 km/s/Mpc. Because published σ values are heterogeneous (direct stellar absorption and calibrated HI/rotation proxies), measurement methodology is treated as a first-class provenance variable and covariance-aware significance tests are reported using the full SH0ES GLS distance-modulus covariance.
Application of the TEP conformal correction Δμ = κ_Cep·S(ρ)·(σ² − σ_ref²)/c²—derived from the TEP period-contraction combined with the virial relation |Φ| ∝ σ²—with Observable Response Coefficient κ_Cep = (1.05 ± 0.43) × 10⁶ mag and effective calibrator reference σ_ref = 75.25 km/s yields a unified local Hubble constant of H0 = 68.17 km/s/Mpc (bootstrap mean 68.14 ± 1.49), corresponding to a Planck tension of 0.49σ. The inferred κ_Cep ~ 10⁶ places this probe in the same response-coefficient regime as the millisecond-pulsar spin-down excess (Paper 10), reducing the apparent cross-probe mismatch at the observable-response level compared with earlier phenomenological log₁₀ σ scalings. Out-of-sample validation (train/test splits and LOOCV) shows that the fitted response coefficient is stable and removes the residual environmental trend in held-out hosts. A differential analysis within M31 yields an "Inner Fainter" signal in HST photometry. Within the TEP v0.8 framework, this sign is consistent with continuous shear suppression: the high-density M31 bulge experiences progressive attenuation of Temporal Shear (suppression factor S ≈ 0.05 at R < 1 kpc), while the lower-density SN Ia host disks remain in the active-shear regime (⟨S⟩ = 0.946). On this interpretation, the M31 signal marks the empirical mapping of a continuous environmental shear-suppression profile across a single galaxy.
The anchor–host mismatch (geometric anchors show near-zero response, κ_anchor = 5.0 ± 663 mag in the σ²/c² convention, with a 2.5σ comparison to the host-level κ_Cep ≈ 1.05 × 10⁶ mag) finds a natural resolution in group halo shear suppression: all three anchors (LMC, NGC 4258, M31) are members of galaxy groups, embedding them in deep ambient potentials that trigger environment-responsive suppression of Temporal Shear regardless of internal disk densities. The SN Ia hosts, selected for smooth Hubble flow, are biased toward isolated field galaxies that lack this external screening. This framework generates a falsifiable prediction: the TEP distance-ladder bias should be unique to isolated field galaxies and suppressed in group/cluster environments.
Analysis of 29 SH0ES Cepheid hosts reveals a significant correlation between derived H₀ and host galaxy velocity dispersion (ρ = 0.511, p = 0.0046). High-σ hosts yield H₀ = 72.45 km/s/Mpc while low-σ hosts yield 67.82 km/s/Mpc—a 4.63 km/s/Mpc environmental bias. Applying the physics-derived TEP conformal correction (κ_Cep ≈ 1.05 × 10⁶ mag with σ²/c² scaling) eliminates this trend, yielding a unified H₀ = 68.17 km/s/Mpc (bootstrap mean 68.14 ± 1.49), reducing Planck tension from 5σ to 0.49σ. A differential analysis within M31 (HST PHAT) detects an "Inner Fainter" signal (+0.68 mag, 3.6σ), explained by density-dependent screening: the high-density bulge is screened while the outer disk is not. The anchor–host mismatch (κ_anchor = 5.0 ± 663 mag vs κ_Cep ≈ 1.05 × 10⁶ mag) is resolved by group halo screening—all anchors reside in galaxy groups, while SN Ia hosts are biased toward isolated field environments.
| Paper | Repository | Title | DOI |
|---|---|---|---|
| Paper 0 | TEP | Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed | 10.5281/zenodo.16921911 |
| Paper 1 | TEP-GNSS | Global Time Echoes: Distance-Structured Correlations in GNSS Clocks | 10.5281/zenodo.17127229 |
| Paper 2 | TEP-GNSS-II | Global Time Echoes: 25-Year Analysis of CODE Precise Clock Products | 10.5281/zenodo.17517141 |
| Paper 3 | TEP-GNSS-RINEX | Global Time Echoes: Raw RINEX Consistency Test | 10.5281/zenodo.17860166 |
| Paper 4 | TEP-GL | Temporal-Spatial Coupling in Gravitational Lensing: A Reinterpretation of Dark Matter Observations | 10.5281/zenodo.17982540 |
| Paper 5 | TEP-GTE | Global Time Echoes: Empirical Synthesis | 10.5281/zenodo.18004832 |
| Paper 6 | TEP-UCD | Universal Critical Density: Cross-Scale Consistency of ρ_T | 10.5281/zenodo.18064365 |
| Paper 7 | TEP-RBH | The Soliton Wake: Exploring RBH-1 as a Temporal Topology Candidate | 10.5281/zenodo.18059250 |
| Paper 8 | TEP-SLR | Global Time Echoes: Optical-Domain Consistency Test via Satellite Laser Ranging | 10.5281/zenodo.18064581 |
| Paper 9 | TEP-EXP | What Do Precision Tests of General Relativity Actually Measure? | 10.5281/zenodo.18109760 |
| Paper 10 | TEP-COS | The Temporal Equivalence Principle: Suppressed Density Scaling in Globular Cluster Pulsars | 10.5281/zenodo.18165798 |
| Paper 11 | TEP-H0 (This repo) | The Cepheid Bias: Resolving the Hubble Tension | 10.5281/zenodo.18209702 |
| Paper 12 | TEP-JWST | The Temporal Equivalence Principle: A Unified Resolution to the JWST High-Redshift Anomalies | 10.5281/zenodo.19000827 |
| Paper 13 | TEP-WB | The Temporal Equivalence Principle: Temporal Shear Recovery in Gaia DR3 Wide Binaries | 10.5281/zenodo.19102061 |
TEP-H0/
├── data/ # Raw and processed data
│ ├── raw/ # Original SH0ES/Gaia datasets
│ ├── processed/ # Stratified and enriched host data
│ └── interim/ # Intermediate calculation files
├── scripts/
│ ├── steps/ # Analysis pipeline steps (1-10)
│ ├── utils/ # Shared utility functions
│ └── analysis/ # Exploratory analysis scripts
├── results/
│ ├── outputs/ # Analysis results (JSON, CSV, Tables)
│ └── figures/ # Generated plots (PNG)
├── site/
│ ├── components/ # Manuscript HTML sections
│ └── public/ # Static assets
├── 11manuscript-tep-h0.md # Full manuscript (Markdown)
└── requirements.txt # Python dependencies
# Clone repository
git clone https://github.com/matthewsmawfield/TEP-H0.git
cd TEP-H0
# Install dependencies
pip install -r requirements.txtresults/outputs/tep_corrected_h0.csv- Final TEP-corrected Hubble Constant values for all hosts.data/processed/hosts_processed.csv- Stratified host galaxy data with velocity dispersions.results/outputs/tep_correction_results.json- Optimized TEP response coefficient (κ_Cep), σ_ref, and statistics.results/outputs/aperture_sensitivity_grid.csv- Sensitivity analysis data for aperture corrections.
The analysis pipeline is fully automated and reproducible. The master script scripts/run_pipeline.py executes the following steps in sequence:
| Manuscript Section | Analysis Step | Script | Description |
|---|---|---|---|
| 2.1 | Data Ingestion | step_1_data_ingestion.py |
Downloads SH0ES/Pantheon+ data, reconstructs catalogs, matches hosts. |
| 2.2 | Aperture Correction | step_1b_aperture_correction.py |
Fetches RC3 metadata and applies aperture normalization to velocity dispersions. |
| 3.1 | Stratification | step_2_stratification.py |
Calculates H₀, stratifies by σ, and detects environmental bias. |
| 3.3 | TEP Correction | step_3_tep_correction.py |
Optimizes κ_Cep, applies the TEP correction, and unifies H₀. |
| 3.6 | Robustness | step_4_robustness_checks.py |
Performs Jackknife, Bootstrap, and Peculiar Velocity Monte Carlo tests. |
| 4.1 | Sensitivity | step_4b_aperture_sensitivity.py |
Tests stability against aperture size and correction parameters. |
| 3.8 | M31 Differential | step_5_m31_analysis.py |
Analyzes Inner vs Outer Cepheids in M31 (Ground-based). |
| 4.2 | Multivariate | step_6_multivariate_analysis.py |
Controls for Age, Dust, and Stellar Mass confounds. |
| 3.8 | LMC Control | step_7_lmc_replication.py |
Replicates differential analysis in LMC (Null Control). |
| 4.8 | M31 PHAT | step_8_m31_phat_analysis.py |
High-resolution HST analysis of M31 Cepheids. |
| Fig 1-9 | Final Synthesis | step_9_final_synthesis.py |
Generates final manuscript figures and summary tables. |
| 3.5 | Anchor Test | step_10_anchor_stratification.py |
Tests for TEP effects in geometric anchors (MW, LMC, N4258). |
To reproduce all results and figures:
python3 scripts/run_pipeline.pyThis will populate results/figures/ and results/outputs/ with fresh data.
To support careful external scrutiny, this repository includes machine-checkable audit artifacts alongside the paper outputs:
- Pipeline audit (sanity checks):
- Run:
python3 scripts/utils/pipeline_audit.py - Purpose: validates internal consistency between key CSV/JSON outputs and critical manuscript values.
- Run:
- Primary audit reports:
AUDIT_REPORT_GENERATED.mdDEEP_AUDIT_REPORT.mdDEEP_AUDIT_LOGIC_REPORT.mdresults/outputs/TEP_FINAL_ROBUSTNESS_REPORT.md
- Hubble-flow SN / redshifts:
data/raw/Pantheon+SH0ES.dat(Pantheon+SH0ES release). - SH0ES host distance moduli: reconstructed from SH0ES R22 inputs (see
data/raw/external/Cepheid-Distance-Ladder-Data/SH0ES2022/). - Velocity dispersions: compiled/regenerated from public catalogs and literature (HyperLEDA, Ho+2009, SDSS; see
data/raw/external/velocity_dispersions_literature*.csv). - M31 HST Cepheids: VizieR catalog
J/ApJ/864/59(Kodric et al. 2018), summarized inresults/outputs/m31_phat_robustness_summary.json.
The analysis demonstrates a statistically significant host-level H₀–σ correlation in the SH0ES host set and shows that a TEP-motivated conformal correction yields a Planck-consistent unified value within uncertainties. The anchor consistency test (LMC, NGC 4258, M31) yields κ_anchor ≈ 0 in the σ²/c² convention and is interpreted through group-halo screening, producing a direct environmental prediction for future field-versus-group distance-ladder tests.
@article{smawfield2026cepheidbias,
title={The Cepheid Bias: Resolving the Hubble Tension},
author={Smawfield, Matthew Lukin},
journal={Zenodo},
year={2026},
doi={10.5281/zenodo.18209702},
note={Preprint v0.6 (Kingston upon Hull)}
}These are working preprints shared in the spirit of open science—all manuscripts, analysis code, and data products are openly available under Creative Commons and MIT licenses to encourage and facilitate replication. Feedback and collaboration are warmly invited and welcome.
Contact: matthew@mlsmawfield.com
ORCID: 0009-0003-8219-3159