What question did this study set out to answer?

This research aims to derive and test observational predictions from a gauge-theoretic framework on spin 4-manifolds.

March 17, 2026Open Access

Gauge Theory on the Metric Bundle of a Spin 4-Manifold, IV: Observational Predictions from Torsion Cosmology, Fiber Dark Energy, and Pati–Salam Unification

Key Points

This research aims to derive and test observational predictions from a gauge-theoretic framework on spin 4-manifolds.
Derived cosmological models from gauge theory framework on metric bundles.
Analyzed data from JWST to address high-redshift galaxy formation time.
Compared dark energy models with DESI DR2 BAO constraints.
Fitted velocity profiles for 175 galaxies using a torsion model against pISO and NFW halo models.
Modified cosmology introduces an effective formation time, alleviating high-redshift galaxy tension.
The derived cosmological constant indicates potential compatibility with dark energy equation of state observations.
Torsion model outperforms NFW halos in fitting galaxy data for 78% of cases, with better median fit quality.
Effective proton stability and seesaw mechanism for neutrinos are resulting features from Pati-Salam symmetry.

Abstract

We derive observational predictions from the gauge-theoretic framework on the metric bundle Y 14 = Met(X4) established in Parts I–III, and confront them with publicly available data. (1) The augmented torsion of Part I, entering the unified action through the term α⟨Taug, εΦ(Taug)⟩ (Part II, Definition 2.1), provides a spin- torsion coupling in the Friedmann equations; we derive the modified cosmology and show that the resulting bounce replaces the Big Bang singularity, adding ∼ 150 Myr of effective formation time that alleviates the high-redshift galaxy tension observed by JWST at z > 7. (2) The effective cosmological constant arises from the intrinsic curvature of the fiber Sym2+(R4) ∼= GL(4)/O(4); we compare with the DESI DR2 BAO constraints on the dark energy equation of state. (3) The conserved spin density from the torsion sector, treated as an extended distribution, produces a velocity profile that is mathematically equivalent to the well-studied pseudo- isothermal (pISO) cored dark matter halo; we fit the full 175-galaxy SPARC catalog with two free parameters per galaxy and find that the torsion model outperforms NFW dark matter halos for 78% of galaxies (with fixed mass-to-light ratios), with median χ2ν = 0.71 (torsion) versus 1.39 (NFW). The physical novelty lies not in the fit quality—which is consistent with existing pISO results in the literature 27, 32—but in the theoretical derivation of the cored profile from the spin-torsion coupling of SGU. (4) The Pati–Salam symmetry-breaking chain yields effective proton stability (τp ≫ 1036 yr), a natural seesaw mechanism for neutrino masses, and distinctive imposter-generation signatures in the third fermion family above the SU(2)R breaking scale.

Gauge Theory on the Metric Bundle of a Spin 4-Manifold, IV: Observational Predictions from Torsion Cosmology, Fiber Dark Energy, and Pati–Salam Unification

Key Points

Abstract

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