BFP Theory: Pantheon+ Light-Speed Evolution Fit (Flagship v15)

This paper presents the foundational framework of the Theory of Base Field Pressure (BFP), a theory in which a single scalar field—the field pressure P—replaces both gravity as a fundamental force and the constancy of the speed of light. All core equations—including the field equation, matter equation of motion, light-speed relation, and Newtonian limit—are derived from a minimal action principle.

## Key Results

### Gravitation and Local Physics- **Field Pressure Domain**: Earth's effective domain radius ≈ 2.59×10⁵ km, consistent with BeiDou satellite orbits and lunar recession (quantitative BFP derivation yields 3.8 cm/yr)- **Classical Tests**: BFP satisfies gravitational lensing (1.75"), GPS time dilation, and binary pulsar orbital decay

### Galaxy and Structure Formation- **SPARC Galaxies**: Field pressure accumulation effect explains flat rotation curves with 97.7% success rate (171/175 galaxies), no dark matter required- **Structure Growth (fσ₈)**: χ²/dof = 0.13 against BOSS/eBOSS/DESI data, reducing S₈ tension from 3.3σ to 2.5σ

### Cosmology- **Pantheon+ Supernovae**: Light-speed evolution model c(z) = c₀(1+z)^{-β} yields H₀ = 71.87 ± 0.26 km/s/Mpc, β = 0.7360 ± 0.0294, χ²_red = 0.478- **Hubble Tension**: BFP prediction passes quantitative test against SH0ES local measurement (χ²/dof = 1.27, p = 0.26, 1.1σ)- **BBN**: Primordial helium-4 abundance Y_p = 0.2482, consistent with observations at 1.1σ- **GW170817**: Low-redshift field pressure saturation naturally satisfies the 10⁻¹⁵ constraint

### Complete Validation MatrixEight independent cosmological tests spanning all cosmic epochs (BBN to present), all with the same fixed parameters (β = 0.7360, Ω_P0 = 0.01, γ = -0.5). No free parameters are adjusted.

## Core Equations

### Light-Speed Evolution```c(z) = c₀(1+z)^{-β}```- β = 0.7360 ± 0.0294 (Pantheon+ calibration)- β > 0 means light speed was slower in the early universe

### Field Pressure Homogenization```H(z) = H₀(1+z)^{3/2}```Derived from the homogenization equation ȮP + 3H_P·P = -Γ(P-P_∞)

### Luminosity Distance (Corrected in v15)```dL = (c₀/H₀)(1+z)[1-(1+z)^{-(β+1/2)}]/(β+1/2)```

### Light-Speed–Field-Pressure Coupling```c(P) = c₀/[1 + λ(P-P_∞)/c₀²]```Four-step derivation provided in Section 2.4.

## Key Updates in v15

1. **Luminosity Distance Formula Correction**: The exponent in Eq. (4.4) has been corrected from (β+3/2) to (β+1/2), matching the integrated result. Verified against the official BFP Pantheon+ fitting script (identical best-fit values).

2. All v14 updates retained:   - Four-step light-speed derivation (Sec. 2.4)   - Dual-path validity conditions (Sec. 2.5.4)   - Lunar recession quantitative derivation (Sec. 2.5.5)   - Non-expanding cosmology clarification (Sec. 4.1–4.2)   - GW170817 low-redshift saturation (Sec. 4.5)   - Appendix B: Gravitational wave equation derivation

## Data Availability

All observational data are publicly accessible:

| Dataset | Link ||---------|------|| SH0ES 2021 | https://doi.org/10.3847/2041-8213/abdbaf || Planck 2018 | https://pla.esac.esa.int/pla/#cosmology || DESI 2025 | https://arxiv.org/abs/2501.01434 || SPARC | http://astroweb.cwru.edu/SPARC/ || Pantheon+ | https://github.com/PantheonPlusSH0ES/DataRelease || LIGO GWOSC | https://www.gw-openscience.org |

All analysis scripts are archived on Zenodo and are fully reproducible.

## Companion Papers (BFP Theory Series: 28 Papers)

| Paper | DOI ||-------|-----|| BBN | [10.5281/zenodo.20540178](https://doi.org/10.5281/zenodo.20540178) || Relay (CAMB + fσ₈) | [10.5281/zenodo.20534820](https://doi.org/10.5281/zenodo.20534820) || Fine-Structure Constant (α) | [10.5281/zenodo.20572878](https://doi.org/10.5281/zenodo.20572878) || Field Pressure Computing | [10.5281/zenodo.20603898](https://doi.org/10.5281/zenodo.20603898) || Mercury & Light Deflection | [10.5281/zenodo.20389787](https://doi.org/10.5281/zenodo.20389787) || Screening Mechanism | [10.5281/zenodo.19920079](https://doi.org/10.5281/zenodo.19920079) || BDS Satellite Clock Rates | [10.5281/zenodo.19920662](https://doi.org/10.5281/zenodo.19920662) |

## Keywords

base field pressure, varying speed of light, modified gravity, scalar field theory, non-expanding cosmology, field pressure homogenization, Pantheon+ supernovae, SPARC galaxy rotation curves, Big Bang nucleosynthesis, Hubble tension, GW170817, field pressure computing, fluctuon bit, attosecond physics

## Citation

```bibtex@article{wang2026bfp,  title={Theory of Base Field Pressure: Foundational Framework and Newtonian Limit (v15)},  author={Wang, Di},  year={2026},  doi={10.5281/zenodo.20673914},  publisher={Zenodo}}```

## License

[CC BY 4.0](https://creativecommons.org/licenses/by/4.0/) — You are free to share and adapt this work, provided you give appropriate credit.

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