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| Hlavní autoři: | , |
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| Médium: | Recurso digital |
| Jazyk: | angličtina |
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Zenodo
2026
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| Témata: | |
| On-line přístup: | https://doi.org/10.5281/zenodo.19876875 |
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- <p><strong>ψ_universe(t) on a compact S³: a causal–geometric cosmology</strong></p> <p>This work presents a compact, geometrically constrained cosmological framework in which the Universe is modelled as a closed three-sphere <strong>S³</strong>, with dynamics governed not by global volume alone, but by a causally accessible domain defined by light propagation. The central distinction is fundamental: <strong>V_obs ≠ V_total</strong>, where the global volume is <strong>V_total = 2π²R³</strong>, while the observable domain is given by <strong>V_obs = 2πR³[χ_L − 1/2 sin(2χ_L)]</strong>, with <strong>χ_L(t) = ∫ c dt′ / R(t′)</strong> acting as the dimensionless causal coordinate.</p> <p>The cosmological state is organised through three coupled fields: the geometric radius <strong>R(t)</strong>, the causal light coordinate <strong>χ_L(t)</strong>, and the energy density <strong>ρ(t)</strong>. This replaces the implicit assumption of instantaneous homogeneity with a dynamically evolving observable structure. The evolution of R(t) follows a two-sector law: an early discrete hierarchy <strong>Rₙ = R₀ φⁿ</strong> (with <strong>φ ≈ 1.618</strong> as the Perron–Frobenius eigenvalue of minimal recursion) and a late-time continuous regime, smoothly connected via <strong>R(t) = R_frac(t)(1 − σ(t)) + R_light(t)σ(t)</strong>. This formulation distinguishes an effective expansion rate <strong>H_eff ≠ H₀</strong>, reflecting long-term geometric growth rather than instantaneous observation.</p> <p>A key conceptual shift lies in the role of light: it is not merely a propagating signal, but the operator that defines the observable Universe. The causal horizon encoded in χ_L(t) determines what portion of S³ is physically accessible at time t. Within this domain, density does not fill space instantaneously, but evolves according to a causal tracking relation <strong>dρ_obs/dt = −Γ(t)[ρ_obs − ρ_total]</strong>, with <strong>Γ(t) = c/(Rχ_L)</strong>, expressing finite propagation of equilibration.</p> <p>Cosmological redshift is reinterpreted as a geometric accumulation along null trajectories rather than a purely kinematic scaling, with <strong>ln(1 + z) = ∫ p(V(r))K(χ(r))/R(r) dr</strong>, where the S³ kernel <strong>K(χ) = 2 sin²χ / (χ − sinχ cosχ)</strong> encodes intrinsic curvature effects. This leads to a window-dependent observational law <strong>H(ℓ) = 3cp/ℓ</strong>, implying that the measured Hubble parameter is not universal but scale-dependent, naturally accommodating the observed ratio <strong>H_late / H_CMB ≈ 1.08–1.10</strong> at a phenomenological level.</p> <p>Importantly, the framework does not claim to derive fundamental constants or replace ΛCDM. Instead, it adopts a consistency-based approach: empirical quantities such as c and H₀ are treated as inputs, and the question becomes whether a compact S³ geometry with causal light fronts admits a coherent internal description. In this sense, relations within the model function as <strong>closure conditions</strong>, not independent predictions.</p> <p>Taken together, this approach offers a unified geometric–causal perspective in which the evolution of <strong>ψ_universe(t)</strong> is not imposed externally, but emerges from the coupled dynamics of space, light, and density within a finite, boundaryless structure.</p> <p><strong> YouTube Podcast: </strong><a href="https://youtube.com/playlist?list=PLzfwBKN-8IjE25FAYnUFoMCqiEjeJ2DH1&si=9wfMYzlxC_-0TdAL" rel="noopener">FB(S³)R — “The Satsang of Reality”</a></p> <ul> <li> ️<a href="https://www.youtube.com/watch?v=eOxGHJ4N5Hw" rel="noopener">Fractal Sphere of Reality. Foundations of the FB(S³)R Model of the Universe</a></li> <li> ️<a href="https://www.youtube.com/watch?v=IVaPRtxnk5o" rel="noopener">Episode 47-SG: Fractal S³ of Reality. The Golden Ratio as the Principle of Perfection</a></li> </ul>