10.5281/zenodo.18806314
The MOND acceleration constant a₀ ≈ 1.2 × 10⁻¹⁰ m/s² is numerically close to cH₀/(2π) — the acceleration associated with the Gibbons–Hawking temperature of the cosmological horizon. This repository tests that coincidence quantitatively against 171 galaxies from the SPARC database and 14 high-redshift galaxies from Genzel et al. (2017, 2020) and Übler et al. (2017).
The derived constant a_u = cH₀/(2π) = 1.04 × 10⁻¹⁰ m/s² outperforms the empirical a₀ = 1.2 × 10⁻¹⁰ m/s² — including within MOND's own interpolation function.
| Configuration | Med χ²/ν | Global free params |
|---|---|---|
| MOND simple + a_u | 1.41 | 0 |
| Holographic + a_u | 1.45 | 0 |
| MOND standard + a₀ | 1.52 | 1 |
| Holographic + a₀ | 1.53 | 1 |
| MOND simple + a₀ | 1.53 | 1 |
| Comparison | Winner | Win rate |
|---|---|---|
| a_u vs a₀ in MOND simple (same function) | a_u | 102/171 (59.6%) |
| a_u vs a₀ in Holographic (same function) | a_u | 104/171 (60.8%) |
| Holographic vs MOND at a₀ (same scale) | Holographic | 113/171 (66.1%) |
| Holographic vs MOND at a_u (same scale) | Holographic | 109/171 (63.7%) |
Both the acceleration scale and the interpolation function independently improve fits. The scale improvement is demonstrable within MOND's own functional form.
The result holds across all error treatments, including raw observational errors with no floor applied (108/171, 63.2% win rate).
14 galaxies at z = 0.9–2.5 from Genzel et al. and Übler et al. show declining outer rotation curves. The a_u(z) framework predicts this: stronger acceleration at high z shrinks the transition radius, leaving the outer galaxy in the Keplerian decline regime. Observed turnover radii cluster tightly around the predicted transition radius r_t(z) = √(GM_b/a_u(z)), with median r_turn/r_t = 0.80.
Standard MOND (constant a₀) predicts the opposite — flat rotation at larger radii at high z.
sparc-gibbons-hawking/
├── README.md
├── LICENSE
├── paper/
│ └── manuscript.md # Full paper (markdown)
├── scripts/
│ ├── sparc_holographic_fit.py # Primary 171-galaxy analysis
│ ├── isolation_test.py # 2×2 scale vs function separation
│ ├── robustness.py # 5 error treatment tests
│ └── high_z_analysis.py # High-z rotation curve test
└── results/
├── fit_summary.csv # Per-galaxy results (all models)
├── global_statistics.txt # Summary statistics
├── highz_summary.txt # High-z analysis summary
├── sparc_figures/ # 7 SPARC figures (PNG + PDF)
└── highz_figures/ # 5 high-z figures (PNG + PDF)
pip install numpy scipy matplotlibDownload SPARC mass models from http://astroweb.cwru.edu/SPARC/
Required file: MassModels_Lelli2016c.mrt (Newtonian Mass Models, Table 2)
Place in a SPARC/ directory alongside the scripts, or edit the file path in each script.
python scripts/sparc_holographic_fit.pypython scripts/isolation_test.pypython scripts/robustness.pypython scripts/high_z_analysis.pyIn de Sitter spacetime, the cosmological horizon has a Gibbons–Hawking temperature T_GH = ℏH/(2πk_B). The associated acceleration is:
a_u = k_B T_GH / (ℏ/c) = cH₀/(2π) ≈ 1.04 × 10⁻¹⁰ m/s²
This is not fitted. It is derived from H₀ = 67.4 km/s/Mpc alone.
The holographic interpolation function:
g_eff = g_N / (1 − exp(−√(|g_N|/a_u)))
has the same Newtonian and deep-MOND limits as standard MOND but transitions more sharply. The 2×2 test shows that both the scale (a_u vs a₀) and the function (holographic vs MOND simple) independently improve fits.
a_u(z) = cH(z)/(2π)
At z = 1: a_u ≈ 1.8× local. At z = 2: a_u ≈ 3.0× local.
This predicts:
- Transition radius shrinks at high z: r_t(z) = √(GM_b/a_u(z))
- Outer rotation curves decline at high z (observed by Genzel et al.)
- BTFR zero-point evolves with H(z)
MOND predicts no evolution (a₀ = constant). CDM predicts halo-dependent evolution unrelated to H(z).
If you use this code or results, please cite the SPARC database:
- Lelli, McGaugh & Schombert, Astron. J. 152, 157 (2016)
MIT