Published July 7, 2026 | Version 1.0

g(z): The Epoch-Dependent Hubble Bias

  • 1. The Resonance Theory Labs

Description

The Hubble tension — the 4.85σ discrepancy between the Planck CMB measurement of H₀ = 67.36 ± 0.54 km/s/Mpc and the SH0ES Cepheid measurement of H₀ = 73.04 ± 1.04 km/s/Mpc — has resisted resolution for over a decade. We derive a function g(z) from the Feigenbaum universality constants α = 2.502907875 and δ = 4.669201609 that predicts precisely what H₀ value each measurement technique extracts from the cascade expansion history as a function of its effective redshift. The two cascade limits are: SH0ES (z → 0): g(0) = 1 + 1/[α(δ+1)] = 1.07047, predicting H₀ = 73.017 km/s/Mpc (residual 0.02σ); Planck (z = 1100): g(1100) = 1 − δ/(α+δ)³ × 0.833, predicting H₀ = 67.491 km/s/Mpc (residual 0.24σ). Both measurements are correct. They are measuring the cascade expansion history at different cosmic epochs. The Hubble tension is resolved: it is not a conflict in measurements but a cascade scale dependence — the same physics that appears in the Eddington staircase (Paper 56) and the cascade Λ derivation (Paper 50). Zero free parameters.

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Additional details

Dates

Created
2027-07-07

Software

Repository URL
https://github.com/lucian-png/resonance-theory-code
Programming language
Python
Development Status
Active

References

  • [P39] Randolph, L. (2026). The Ghost Complete Model: All Six ΛCDM Parameters Derived from One Constant and One Measurement. DOI: 10.5281/zenodo.19416496
  • [P50] Randolph, L. (2026). The Cascade Energy Staircase: Dissolution of the Hierarchy Problem, the Cosmological Constant, and the Emergence of QCD from Electroweak Symmetry Breaking. DOI: 10.5281/zenodo.20386339
  • [P56] Randolph, L. (2026). The Eddington Cascade. Resonance Theory Laboratory. DOI: 10.5281/zenodo.21247098
  • [P57] Randolph, L. (2026). Super-ΛCDM: The Cascade Architecture of Cosmic Evolution. Resonance Theory Laboratory. DOI: 10.5281/zenodo.21247100
  • [SH0ES] Riess, A.G. et al. (2022). A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team. ApJ Letters 934, L7.
  • [Planck] Planck Collaboration (2020). Planck 2018 results. VI. Cosmological parameters. A&A 641, A6.
  • [DESI] DESI Collaboration (2024). DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations. arXiv:2404.03002.