The Kerr-Salpeter 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, 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 replaced by a non-singular spin-torsion bounce driven by fermionic coupling at the Cartan density limit. Through irreducible tensor decomposition, we mathematically prove that quantum vacuum viscosity exponentially damps the highly anisotropic Kantowski-Sachs shear (e^-32K). This dynamically isolates a strictly isotropic trace tensor that natively mimics a cosmological constant (₄₅₅), yielding an effective pseudo-FLRW expansion 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, and dynamically extracts excess angular momentum. This guarantees the stable, 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. Section 11 Geometric Dark Energy: We provide analytical proof that the late-time accelerated expansion (initiating at z 0. 63) is not driven by vacuum energy. It is the mandatory kinematic consequence of the comoving spatial slice crossing the inherent centrifugal repulsive threshold (rₑ₄₏ = 1. 0 Rg) of the parent Kerr geometry. This topological transition is an exact invariant dictated by the universal Kerr identity and constrained by the Thorne limit. Section 12 The Hubble Tension (H₀): The severe discrepancy between local (SH0ES) and global (Planck) expansion rates is rigorously resolved as an optical projection effect. By deriving the macroscopic Fermat optical metric for the interior domain, we prove that residual kinematic shear acts as a gravitational refractive index. Integrating the squared shear perturbation along the conformal domain yields the exact statistical variance of a uniform distribution (1/12). This establishes a rational topological elongation invariant (= 13/12 1. 0833), perfectly recovering the observed H₀ anomaly without altering intrinsic CMB plasma physics. What's New in This Major Revision: This version elevates the Kerr-Salpeter framework from a phenomenological model to a rigorous analytical theory. Key mathematical upgrades include: Formal Optic Derivation: The phenomenological H₀ tension resolution is now formally grounded in the Fermat optical metric and Zalaletdinov’s Covariant Macroscopic Gravity. The factor 13/12 is rigorously proven to be the exact geometric variance of the normalized shear profile. Irreducible Tensor Decomposition: The apparent paradox between the isotropic expansion (₄₅₅) and the residual anisotropic shear (causing the CMB quadrupole and H₀ tension) is resolved via strict algebraic decomposition, proving compatibility with Planck's constraints. Parameter-Free Dynamics: The derivations of the Tully-Fisher relation and the conformal redshift mapping (1+z = ₀/) are now entirely decoupled from empirical inputs, confirming the strictly deterministic and topological nature of the model. Note on Manuscript Status (Living Document): This preprint is maintained as a "living document. " Because the Kerr-Salpeter framework yields strictly deterministic predictions across multiple interconnected domains of astrophysics, the theoretical edifice is continually being expanded. Future versions—integrating additional analytical derivations—will be versioned and published directly under this exact Zenodo record. 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.