What question did this study set out to answer?

The research aims to derive the Hubble constant using fundamental constants and a model-independent observation.

April 18, 2026Open Access

The Speed Gap: A Scaling Framework from Atomic Constants to the Hubble Constant

Key Points

The research aims to derive the Hubble constant using fundamental constants and a model-independent observation.
Derivation of H₀ from five fundamental constants and one CMB observation.
Application of the Speed Gap principle relating to gravitational stability and scale-dependent coupling.
Utilization of the identiy related to sphere geometry for the dark energy exponent derivation.
Comparison of observational data with prior models, specifically ΛCDM and standard Friedmann.
H₀ is calculated to be 70.05 km s⁻¹ Mpc⁻¹, matching recent measurements closely.
Dark energy fraction found to be 0.7216, while the matter fraction is 0.2784.
CMB angular scale reproduction is achieved to within 0.094%, indicating high precision.
Analysis shows preference for the proposed framework over ΛCDM in multiple observations.

Abstract

We present a self-contained derivation of the Hubble constant H₀ = 70. 05 km s⁻¹ Mpc⁻¹ from five fundamental constants (α, G, ℏ, c, mₑ) and one model-independent CMB observation (θ* = 0. 5965°). The derivation requires no freely adjustable cosmological parameters. Starting from the Speed Gap principle (gravitational stability when field-demanded speed matches actual speed), we show that the same condition with scale-dependent coupling Gₑff governs systems from nuclear binding to galactic rotation. The dark energy exponent p = e^ (-3/4) = 0. 4724 is derived from D = 3 sphere geometry through the identity 4/3 × 3/4 = 1. The matter fraction Ωₘ = (1-p) ² = 0. 2784 and dark-energy fraction ΩDE = p (2-p) = 0. 7216 = OE (βcosmic=0. 6808) follow as virial complementarity. The differential form of A+B=1, namely ΔA+ΔB=0, constrains the background to standard Friedmann. Unmodified CLASS reproduces the CMB angular scale to 0. 094%, S₈ = 0. 775 matches DES Y3 to 0. 07σ, and DESI DR1 BAO distances favour the framework (χ²/N = 1. 51) over ΛCDM (1. 79). H₀ = 70. 05 matches TRGB (Freedman 2024) to 0. 1σ and DESI + DES PEDE to 0. 01σ. This V4 supersedes V3 (10. 5281/zenodo. 19244123): the modified Friedmann of V3 §5. 7 violated A+B=1 and has been replaced by standard Friedmann, derived in the companion paper Singh 2026g (10. 5281/zenodo. 19383758).

The Speed Gap: A Scaling Framework from Atomic Constants to the Hubble Constant

Key Points

Abstract

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