The Kerr-Cartan Cosmological Model: Geometric Unification of Cosmological Anomalies

This manuscript proposes a unified cosmological framework grounded in a single, strictly geometric postulate: our observable universe resides within the interior of a hyper-massive, near-extremal Kerr black hole naturally constrained at the Thorne astrophysical limit (a_* = 0. 998). Applying Occam's Razor to modern cosmology, this model sharply contrasts with the standard CDM paradigm, which continuously requires the addition of ad hoc, unobserved parameters (e. g. , scalar inflaton fields, vacuum dark energy, new physics beyond the Standard Model) to reconcile theory with observational data. Instead, we demonstrate that a purely geometric approach is sufficient. By applying the established laws of General Relativity, Covariant Macroscopic Gravity (CMG), and the Einstein-Cartan-Sciama-Kibble (ECSK) theory to a rotating black hole interior, the entirety of current cosmological anomalies can be resolved through pure physical determinism. To facilitate mathematical verification, this manuscript is structured to demonstrate exactly how internal rotational dynamics systematically resolve these specific crises. Readers can refer directly to the following sections for analytical proofs: Sections 3, 5 & 6 The Singularity, Inflation, and Isotropization: The classical Riemann singularity is formally prohibited and replaced by a non-singular spin-torsion bounce driven by Weyssenhoff fluid dynamics at the exact Cartan density limit (C 3. 7 10^58 kg m^-3). Through irreducible tensor decomposition, we mathematically prove that quantum vacuum viscosity exponentially damps the highly anisotropic Kantowski-Sachs kinematic shear (e^-64K). This isolates a strictly isotropic trace tensor that natively mimics a cosmological constant (₄₅₅) without hypothetical scalar inflatons. Section 10 The JWST Crisis and Galaxy Formation: The residual Lense-Thirring frame-dragging field exerts a critical macroscopic geodetic torque on collapsing primordial halos. We analytically demonstrate that this spin-orbit coupling lowers the critical Kerr-Jeans mass threshold by 95\% at z > 20. This guarantees the accelerated, monolithic collapse of hyper-massive galaxies at the Cosmic Dawn, natively yielding the parameter-free Tully-Fisher relation (v_ M^1/3) without requiring cold dark matter halos. Section 11 Geometric Dark Energy & Topological Equipartition: We provide analytical proof that the late-time accelerated expansion is not driven by vacuum energy. It is the mandatory kinematic consequence of the comoving spatial slice crossing the inherent centrifugal repulsive threshold of the Kerr geometry (ₑ₄₏ 0. 5316). Furthermore, the present-day observer coordinate is rigorously derived from the R S² topological dimensional equipartition (₀ = 2/3), natively predicting the onset of acceleration at z₀₂₂ 0. 63 without any empirical fitting parameters. Section 12 The Hubble (H₀) and S₈ Tensions: The severe discrepancy between local and global expansion rates is rigorously resolved as a macroscopic optical projection effect. By utilizing Zalaletdinov’s Covariant Macroscopic Gravity, we derive the exact invariant = 13/12 1. 0833, which flawlessly recovers the H₀ anomaly. Crucially, this version includes new numerical validation: we demonstrate through MCMC (Monte Carlo Markov Chain, Section 15) sampling that the modified Hubble friction—inherent to the Kerr-Cartan expansion history—suppresses the growth of matter fluctuations. This provides a simultaneous, parameter-free resolution to the S₈ clustering tension observed in weak-lensing surveys (KiDS-1000/DES). This version elevates the Kerr-Cartan framework from a phenomenological model to a strictly deterministic analytical theory. Key mathematical upgrades include: MCMC Numerical Validation: Implementation of the geometric elongation into the CLASS cosmological solver. High-likelihood MCMC chains confirm that the model natively resolves both the H₀ and S₈ tensions using only the topological Thorne limit (a_* = 0. 998). Covariant Macroscopic Optics: Eradication of the divergent stationary Fermat metric. The = 13/12 optical deformation is now formally derived as the exact affine connection correlation tensor Z in CMG. Eradication of Empirical Fits: The observer conformal coordinate (₀) is no longer fitted to z₀₂₂, but strictly derived from spatial equipartition (₀ = 2/3). Tensor Decoupling: Added rigorous algebraic decomposition proving that kinematic shear (_, satisfying Planck limits) is completely decoupled from topological frame-dragging (_, causing the H₀ anomaly). S₈ Tension Resolution: Implementation of the geometric elongation into the CLASS cosmological solver, confirming via MCMC that the modified Hubble friction mechanically resolves the S₈ clustering anomaly. Corresponding Author: Flavio Gomes (f. gomes. phys@proton. me). Scientific inquiries, rigorous peer-reviews, and collaborative proposals regarding the Kerr-Cartan mathematical framework or its observational predictions are actively welcomed.