Absolute Cosmic Geometry: First-Principles Derivation of 5D Topological Self-Acceleration and the Exact Resolution of the Hubble H0 Tension
Year: 2026
Type: preprint
Abstract: ### الملكية الفكرية وإشعار الأولوية العلمية © 2026 Saif M. Al-Muazzab. All Rights Reserved. This repository serves as an official timestamped deposition securing the Intellectual Property (IP), mathematical derivations, and 10 falsifiable observational predictions authored by Saif M. Al-Muazzab regarding the 5D Topological Self-Acceleration Framework (Absolute Cosmic Geometry). --- ### KEY MATHEMATICAL & THEORETICAL INNOVATIONS (Protected IP): 1. First-principles projection of the 5D Einstein-Gauss-Bonnet (EGB) bulk action onto a 4D FLRW brane via Gauss-Codazzi-Mainardi formalism and generalized Myers-Davis junction conditions. 2. Derivation of the exact non-linear modified Friedmann equation: H²(1 + 4/3 α̂ H²)² = (κ₅² / 6 ρ + ... )² 3. Analytical derivation of the late-time geometric boost factor δGB(z), resolving the 5σ Hubble tension (H0 = 73.12 ± 0.68 km/s/Mpc) without modifying the sound horizon (rs = 147.09 Mpc). --- ### TEN FALSIFIABLE OBSERVATIONAL PREDICTIONS (Scientific Priority Claim): 1. Exact Local Hubble: Permanent convergence at H0 = 73.12 ± 0.68 km/s/Mpc. 2. Transition Redshift: Topological boost derivative z_trans = 0.85 ± 0.05. 3. Invariant Sound Horizon: Strictly fixed at rs = 147.09 ± 0.26 Mpc. 4. Tensor Velocity: Local cT = c, with Weyl phase shift ΔcT/c < 10⁻¹⁵ at z > 2. 5. Ghost-Free Phantom Crossing: Effective equation of state w_eff(z) dynamically crosses -1 via geometry. 6. Simultaneous S8 Resolution: Growth suppression yielding σ8 = 0.762 ± 0.008. 7. LSST+Euclid Constraints: Cosmic shear C_l^(γγ) 4.2σ geometric deviation at l > 1500. 8. JWST High-z Overdensities: Growth factor D(z) enhanced by 12–15% at z > 7. 9. Weyl Dark Radiation: Bulk integration bounds ΔN_eff ≤ 0.035 (CMB-S4 target). 10. Fundamental Coupling: EGB coupling constant α̂ = 0.0412 ± 0.0035. Author: Saif M. Al-Muazzab (Independent Researcher, Cosmology and Astrophysics, Sana'a, Yemen). License: Creative Commons Attribution 4.0 International (CC BY 4.0) - Citation required upon use. The persistent 5σ tension between early-universe inferences of the Hubble constant (H0) and late-universe local measurements signifies a fundamental failure of the four-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) paradigm. In this comprehensive treatise, we demonstrate from first epistemological principles that the H0 discrepancy is a direct manifestation of 5D topological boundary dynamics. By projecting the 5D Riemann tensor via the complete Gauss-Codazzi-Mainardi formalism and applying exact generalized Myers-Davis junction conditions, we derive the exact, non-linear modified Friedmann equation from the Einstein-Gauss-Bonnet (EGB) action. The topological self-acceleration branch induces a late-time geometric deformation δGB(z) that elevates the local H0 to 73.12 km s⁻¹ Mpc⁻¹ while strictly preserving the comoving sound horizon rs. A joint MCMC analysis of Planck 2018, DESI 2024 BAO, and local distance ladder data confirms the complete resolution of the tension. We formulate ten stringent observational predictions, including combined LSST+Euclid cosmic shear constraints, offering a definitive geometric solution to the H0 crisis.
Author: Al-Muaazab, Saif mohammed
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204209160
Cites:
Cited by:
Related to: