What question did this study set out to answer?

This work aims to extend the Expansion Freedom Principle by introducing geometry-dependent flux areas and unifying inertial motion principles.

June 14, 2026Open Access

The Expansion Freedom Principle v6.2: Hierarchical Effective Flux Areas, Generalized Inertial Motion, Natural Gravitational Boundaries, and the Hubble Tension

Key Points

This work aims to extend the Expansion Freedom Principle by introducing geometry-dependent flux areas and unifying inertial motion principles.
Developed a hierarchical model for effective flux areas across various geometric systems.
Introduced new definitions for inertial motion and gravitational influence boundaries verified across different cosmic scales.
Compiled a two-component expansion model to contextualize the Hubble tension through void-fraction evolution.
The generalized effective flux areas imply dark matter as a remnant from non-spherical geometries, impacting structure formation.
Natural gravitational boundaries were established, removing the necessity of dark energy in cosmological models.
Quantified the Hubble tension as a natural effect of void evolution with a directional anisotropy of H0 significant at 3.9 sigma.

Abstract

This paper extends the Expansion Freedom Principle (v6. 1) with four major developments. First, the effective flux area Aₑff is generalised across a hierarchy of system geometries: spherical bodies (Aₑff = 4π*r²), spiral-galaxy disks (Aₑff = 4π*Hₑff*r, recovering flat rotation curves), filaments (cross-section Aₑff = Hₑff², giving constant g), and galaxy-cluster nodes (Aₑff = n*Hₑff²). This replaces the single isotropic-propagation assumption with geometry-dependent flux distribution. Dark matter is shown to be the residual of applying spherical Aₑff to non-spherical systems. Second, inertial motion is generalised to the condition aₘatter = const, aᵣelativewithₛystem = 0, unifying Galilean straight-line inertia with circular inertial motion at galactic outskirts, and clarifying that solar-system orbits (forced motion) and galactic flat rotation (inertial motion) are fundamentally different phenomena historically conflated under Keplerian dynamics. Third, each mass is shown to possess a natural boundary of gravitational influence at rbalance = (GM/H²) ^ (1/3), verified at both solar-system (Oort Cloud) and galactic (virial radius) scales. Beyond this boundary, matter joins the Hubble flow. This natural boundary, absent in Newtonian gravity, eliminates the need for dark energy or a cosmological constant. A minimum-aₘatter principle is introduced to explain mass-centre selection, self-reinforcing structure formation, and the separation of stellar clumps without invoking repulsion. Fourth, a two-component expansion model (H = fᵥoid * Hᵥoid + fₘatter * Hₘatter) quantifies the Hubble tension as a natural consequence of void-fraction evolution rather than unresolved physics, consistent with the observed directional anisotropy of H0 (Cosmicflows-4, 3. 9 sigma). The light-deflection result 4GM/ (c² b) is given a physical derivation as two equal effects of an expanding source body: its surface approaching the light ray, and its surface flattening as it expands, explaining for the first time, in elementary terms, why GR's prediction is exactly twice Newton's. Throughout, spacetime is treated as a map constructed to interpret expansion, with dark matter, dark energy, and the Hubble tension identified as Mercator-type projection artefacts of that map.

The Expansion Freedom Principle v6.2: Hierarchical Effective Flux Areas, Generalized Inertial Motion, Natural Gravitational Boundaries, and the Hubble Tension

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