Relativity and Cosmology

   

Hierarchical Geometric Cosmology with Einstein-Cartan Torsion: A Unified Framework for the Cosmological Constant, Dark Matter, and Baryogenesis

Authors: Vito Uni

We present Hierarchical Geometric Cosmology (HGC v3.0), a framework that addresses three of the deepest open problems in modern cosmology — the cosmological constant, the nature of dark matter, and the matter-antimatter asymmetry — within a single geometric structure. The central premise is that our universe occupies the interior of a rotating black hole embedded in a parent spacetime governed by Einstein-Cartan theory, which extends General Relativity by incorporating the spin of matter as a source of spacetime torsion.The cosmological constant emerges naturally from the Israel-Darmois junction conditions at the black hole horizon, yielding Λ_eff = ζ Φ(a*)/R_s², where R_s is the Schwarzschild radius of the parent black hole and Φ(a*) encodes the spin contribution. With R_s ~ R_H, this produces the observed order of magnitude (10u207bu2075² mu207b²) without fine-tuning, resolving the 120-order-of-magnitude discrepancy with quantum field theory predictions.The Big Bang singularity is replaced by a torsion-induced bounce at the Cartan density ρ_C ~ 10u2076u2076 kg/m³, a semiclassical process some 30 orders of magnitude below the Planck scale. Numerical integration of the Kantowski-Sachs equations through the bounce shows that all initial conditions converge to an isotropic FRW universe with f_iso = 0.334 ± 0.001, independent of initial anisotropy.Dark matter halos are replaced by a gravitational shadowing potential derived from Regge-Wheeler/Zerilli tidal perturbation theory, with a characteristic scale r_c = R_s/√6. This model is tested against the full SPARC database of 175 disk galaxies, achieving a median χ²_r = 2.09 and performing comparably to NFW dark matter profiles (49 vs. 59 galaxy wins). The critical observational distinction lies at scales R > 2 Mpc, where shadowing predicts 5—15% suppression in weak gravitational lensing relative to NFW — a test accessible to Euclid and LSST.For baryogenesis, the cubic torsion term in the Dirac equation produces a mass asymmetry between matter and antimatter. We report honestly that the perturbative calculation yields δM/m ~ 10u207bu2076u2076 at the electroweak scale, far below the observed baryon asymmetry η_B ~ 6 × 10u207b¹u2070. We identify non-perturbative torsion effects near the Cartan density as the most plausible resolution and retain this as an open theoretical direction.Three primary open problems are explicitly identified: (i) the parameter ζ is geometrically motivated but not fully derived from first principles, with a factor ~4 gap remaining; (ii) HGC and NFW are statistically indistinguishable at the rotation curve level; (iii) torsion baryogenesis is qualitatively valid but quantitatively insufficient in the perturbative regime. Seven falsifiable predictions are presented for LiteBIRD, Euclid, LISA, DESI, CERN ALPHA/BASE, and JWST.

Comments: 24 Pages.

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Submission history

[v1] 2026-02-27 01:03:26
[v2] 2026-05-21 09:37:07

Unique-IP document downloads: 274 times

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