The Kerr-Cartan Cosmological Model: Geometric Unification of Cosmological Anomalies
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2026
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| _version_ | 1866902027412439040 |
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| author | Gomes, Flavio |
| author_facet | Gomes, Flavio |
| contents | <p>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 (<span class="math-inline">$a_* = 0.998$</span>).</p> <p>Applying Occam's Razor to modern cosmology, this model sharply contrasts with the standard <span class="math-inline">$\Lambda$</span>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.</p> <p>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:</p> <ul> <li> <p><strong>[Sections 3, 5 & 6] The Singularity, Inflation, and Isotropization:</strong> 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 (<span class="math-inline">$\rho_C \approx 3.7 \times 10^{58} \text{ kg m}^{-3}$</span>). Through irreducible tensor decomposition, we mathematically prove that quantum vacuum viscosity exponentially damps the highly anisotropic Kantowski-Sachs kinematic shear (<span class="math-inline">$e^{-64\mathcal{K}}$</span>). This isolates a strictly isotropic trace tensor that natively mimics a cosmological constant (<span class="math-inline">$\Lambda_{eff}$</span>) without hypothetical scalar inflatons.</p> </li> <li> <p><strong>[Section 10] The JWST Crisis and Galaxy Formation:</strong> 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 <span class="math-inline">$\sim 95\%$</span> at <span class="math-inline">$z > 20$</span>. This guarantees the accelerated, monolithic collapse of hyper-massive galaxies at the Cosmic Dawn, natively yielding the parameter-free Tully-Fisher relation (<span class="math-inline">$v_\infty \propto M^{1/3}$</span>) without requiring cold dark matter halos.</p> </li> <li> <p><strong>[Section 11] Geometric Dark Energy & Topological Equipartition:</strong> 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 (<span class="math-inline">$\chi_{rep} \approx 0.5316$</span>). Furthermore, the present-day observer coordinate is rigorously derived from the <span class="math-inline">$\mathbb{R} \times S^2$</span> topological dimensional equipartition (<span class="math-inline">$\chi_0 = \sqrt{2/3}$</span>), natively predicting the onset of acceleration at <span class="math-inline">$z_{acc} \approx 0.63$</span> without any empirical fitting parameters.</p> </li> <li> <p><strong>[Section 12] The Hubble (<span class="math-inline">$H_0$</span>) and <span class="math-inline">$S_8$</span> Tensions:</strong> 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 <span class="math-inline">$\Gamma = 13/12 \approx 1.0833$</span>, which flawlessly recovers the <span class="math-inline">$H_0$</span> 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 <span class="math-inline">$S_8$</span> clustering tension observed in weak-lensing surveys (KiDS-1000/DES).</p> </li> </ul> <p><strong>What's New in Version 11 (Major Analytical Upgrade):</strong></p> <p>This version elevates the Kerr-Cartan framework from a phenomenological model to a strictly deterministic analytical theory. Key mathematical upgrades include:</p> <ul> <li><strong>MCMC Numerical Validation:</strong> Implementation of the <span class="math-inline">$\Gamma$</span> geometric elongation into the CLASS cosmological solver. High-likelihood MCMC chains confirm that the model natively resolves both the <span class="math-inline">$H_0$</span> and <span class="math-inline">$S_8$</span> tensions using only the topological Thorne limit (<span class="math-inline">$a_* = 0.998$</span>).</li> <li> <p><strong>Covariant Macroscopic Optics:</strong> Eradication of the divergent stationary Fermat metric. The <span class="math-inline">$\Gamma = 13/12$</span> optical deformation is now formally derived as the exact affine connection correlation tensor <span class="math-inline">$\langle Z \rangle$</span> in CMG.</p> </li> <li> <p><strong>Eradication of Empirical Fits:</strong> The observer conformal coordinate (<span class="math-inline">$\chi_0$</span>) is no longer fitted to <span class="math-inline">$z_{acc}$</span>, but strictly derived from spatial equipartition (<span class="math-inline">$\chi_0 = \sqrt{2/3}$</span>).</p> </li> <li> <p><strong>Tensor Decoupling:</strong> Added rigorous algebraic decomposition proving that kinematic shear (<span class="math-inline">$\sigma_{\mu\nu}$</span>, satisfying Planck limits) is completely decoupled from topological frame-dragging (<span class="math-inline">$\tilde{\omega}_{\mu\nu}$</span>, causing the <span class="math-inline">$H_0$</span> anomaly).</p> </li> <li> <p><strong><span class="math-inline">$S_8$</span> Tension Resolution:</strong> Implementation of the <span class="math-inline">$\Gamma$</span> geometric elongation into the CLASS cosmological solver, confirming via MCMC that the modified Hubble friction mechanically resolves the <span class="math-inline">$S_8$</span> clustering anomaly.</p> </li> </ul> <p><strong>Note on Manuscript Status (Living Document):</strong> This preprint is maintained as a "living document." Because the Kerr-Cartan framework yields strictly deterministic predictions across multiple interconnected domains of astrophysics, the theoretical edifice is continually being expanded. Future versions will be versioned and published directly under this exact Zenodo record.</p> <p><em>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.</em></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19658554 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Kerr-Cartan Cosmological Model: Geometric Unification of Cosmological Anomalies Gomes, Flavio Black Hole Cosmology Dark Energy Kerr Metric Centrifugal Force Salpeter Time Big Rip Alternative Cosmology S8 Tension Salpeter Accretion hubble tension hubble Kerr-Cartan Kerr-Salpeter <p>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 (<span class="math-inline">$a_* = 0.998$</span>).</p> <p>Applying Occam's Razor to modern cosmology, this model sharply contrasts with the standard <span class="math-inline">$\Lambda$</span>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.</p> <p>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:</p> <ul> <li> <p><strong>[Sections 3, 5 & 6] The Singularity, Inflation, and Isotropization:</strong> 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 (<span class="math-inline">$\rho_C \approx 3.7 \times 10^{58} \text{ kg m}^{-3}$</span>). Through irreducible tensor decomposition, we mathematically prove that quantum vacuum viscosity exponentially damps the highly anisotropic Kantowski-Sachs kinematic shear (<span class="math-inline">$e^{-64\mathcal{K}}$</span>). This isolates a strictly isotropic trace tensor that natively mimics a cosmological constant (<span class="math-inline">$\Lambda_{eff}$</span>) without hypothetical scalar inflatons.</p> </li> <li> <p><strong>[Section 10] The JWST Crisis and Galaxy Formation:</strong> 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 <span class="math-inline">$\sim 95\%$</span> at <span class="math-inline">$z > 20$</span>. This guarantees the accelerated, monolithic collapse of hyper-massive galaxies at the Cosmic Dawn, natively yielding the parameter-free Tully-Fisher relation (<span class="math-inline">$v_\infty \propto M^{1/3}$</span>) without requiring cold dark matter halos.</p> </li> <li> <p><strong>[Section 11] Geometric Dark Energy & Topological Equipartition:</strong> 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 (<span class="math-inline">$\chi_{rep} \approx 0.5316$</span>). Furthermore, the present-day observer coordinate is rigorously derived from the <span class="math-inline">$\mathbb{R} \times S^2$</span> topological dimensional equipartition (<span class="math-inline">$\chi_0 = \sqrt{2/3}$</span>), natively predicting the onset of acceleration at <span class="math-inline">$z_{acc} \approx 0.63$</span> without any empirical fitting parameters.</p> </li> <li> <p><strong>[Section 12] The Hubble (<span class="math-inline">$H_0$</span>) and <span class="math-inline">$S_8$</span> Tensions:</strong> 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 <span class="math-inline">$\Gamma = 13/12 \approx 1.0833$</span>, which flawlessly recovers the <span class="math-inline">$H_0$</span> 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 <span class="math-inline">$S_8$</span> clustering tension observed in weak-lensing surveys (KiDS-1000/DES).</p> </li> </ul> <p><strong>What's New in Version 11 (Major Analytical Upgrade):</strong></p> <p>This version elevates the Kerr-Cartan framework from a phenomenological model to a strictly deterministic analytical theory. Key mathematical upgrades include:</p> <ul> <li><strong>MCMC Numerical Validation:</strong> Implementation of the <span class="math-inline">$\Gamma$</span> geometric elongation into the CLASS cosmological solver. High-likelihood MCMC chains confirm that the model natively resolves both the <span class="math-inline">$H_0$</span> and <span class="math-inline">$S_8$</span> tensions using only the topological Thorne limit (<span class="math-inline">$a_* = 0.998$</span>).</li> <li> <p><strong>Covariant Macroscopic Optics:</strong> Eradication of the divergent stationary Fermat metric. The <span class="math-inline">$\Gamma = 13/12$</span> optical deformation is now formally derived as the exact affine connection correlation tensor <span class="math-inline">$\langle Z \rangle$</span> in CMG.</p> </li> <li> <p><strong>Eradication of Empirical Fits:</strong> The observer conformal coordinate (<span class="math-inline">$\chi_0$</span>) is no longer fitted to <span class="math-inline">$z_{acc}$</span>, but strictly derived from spatial equipartition (<span class="math-inline">$\chi_0 = \sqrt{2/3}$</span>).</p> </li> <li> <p><strong>Tensor Decoupling:</strong> Added rigorous algebraic decomposition proving that kinematic shear (<span class="math-inline">$\sigma_{\mu\nu}$</span>, satisfying Planck limits) is completely decoupled from topological frame-dragging (<span class="math-inline">$\tilde{\omega}_{\mu\nu}$</span>, causing the <span class="math-inline">$H_0$</span> anomaly).</p> </li> <li> <p><strong><span class="math-inline">$S_8$</span> Tension Resolution:</strong> Implementation of the <span class="math-inline">$\Gamma$</span> geometric elongation into the CLASS cosmological solver, confirming via MCMC that the modified Hubble friction mechanically resolves the <span class="math-inline">$S_8$</span> clustering anomaly.</p> </li> </ul> <p><strong>Note on Manuscript Status (Living Document):</strong> This preprint is maintained as a "living document." Because the Kerr-Cartan framework yields strictly deterministic predictions across multiple interconnected domains of astrophysics, the theoretical edifice is continually being expanded. Future versions will be versioned and published directly under this exact Zenodo record.</p> <p><em>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.</em></p> |
| title | The Kerr-Cartan Cosmological Model: Geometric Unification of Cosmological Anomalies |
| topic | Black Hole Cosmology Dark Energy Kerr Metric Centrifugal Force Salpeter Time Big Rip Alternative Cosmology S8 Tension Salpeter Accretion hubble tension hubble Kerr-Cartan Kerr-Salpeter |
| url | https://doi.org/10.5281/zenodo.19658554 |