Hubble Parameter

H₀ from the S³ curvature radius. The Mach closure condition gives R_U = √6 c/H₀. The Hubble tension may reflect the incorrect assumption of a flat universe in an S³ geometry.

The Hubble parameter is fundamentally linked to the geometry of the universe in the CPT framework. Rather than being merely an empirical parameter describing expansion, it emerges from the Mach closure condition and the intrinsic curvature of S³.

The Mach-H₀ Connection

The Mach closure condition dictates that . Evaluating the S³ Friedmann equation at the expansion maximum (the turning point where ) yields a direct relationship between the Hubble scale and the curvature radius: .

However, the full M13 derivation incorporates the double-copy packing factor, yielding the precise correction:

Curvature Radius

Using an estimated baryonic mass , this relation predicts , effectively spanning the range of current measurements depending on the specific assumptions made regarding dark matter content.

Resolving the Hubble Tension

A major crisis in modern cosmology is the "Hubble Tension": CMB measurements (Planck) infer , while local distance ladder measurements (Cepheids/Supernovae) find .

Radius Estimate

The CPT framework suggests this tension may be a systematic error arising from applying flat-universe (CDM) equations to a genuinely curved S³ universe. The intrinsic curvature modifies the angular diameter distance–redshift relation, natively leading to differing apparent values depending on the measurement scale.

Integrity Status [M]: Maturing

Once the S³ Friedmann equation is fully solved incorporating the rigorous Weber-derived matter density evolution, should become a uniquely predicted parameter rather than an input.

Source Documents

The primary research documents underlying this page. All files are freely viewable and downloadable. They represent the working research as written — including integrity tags, equations, and finding IDs.

Documents open in the CPT Research Library — a formatted viewer for all source research files.