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| Main Authors: | , |
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| Formato: | Recurso digital |
| Idioma: | inglés |
| Publicado: |
Zenodo
2025
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| Subjects: | |
| Acceso en liña: | https://doi.org/10.5281/zenodo.15486751 |
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Table of Contents:
- <p>The <strong>wave function: ψuniverse(t)</strong> in the <strong>Fractal Bindu (S³) of Reality</strong> offers a paradigm shift in our understanding of cosmology. Unlike ΛCDM, which relies on empirically fitted parameters, this model emerges from a single, mathematically coherent framework: a compact, three-dimensional sphere (<strong>S³</strong>) where energy, space, and time evolve through fractal self-organization.</p> <p><strong>Rooted in the golden ratio </strong>ϕ≈1.618\phi \approx 1.618ϕ≈1.618 this theory replaces <strong>arbitrary cosmological constants</strong> with a natural, recursive structure that predicts the evolution of energy density <strong>without dark energy</strong>.</p> <p>The Universe unfolds in <strong>two fundamental phases</strong>:</p> <ol> <li><strong>A pre-recombination fractal expansion</strong> governed by R(t)=lP⋅ϕN(t)R(t) = l_P \cdot \phi^{N(t)}R(t)=lP⋅ϕN(t) where N(t)N(t)N(t) is the discrete fractal level at time ttt.</li> <li><strong>A post-recombination exponential growth</strong> following R(t)=Rrec⋅eH(t−trec)R(t) = R_{\text{rec}} \cdot e^{H (t - t_{\text{rec}})}R(t)=Rrec⋅eH(t−trec) where <strong>energy remains fixed</strong> at Etotal=7.21×1069 J.E_{\text{total}} = 7.21 \times 10^{69} \text{ J}.Etotal=7.21×1069 J.</li> </ol> <p>This leads directly to the <strong>precise observed values</strong>:</p> <ul> <li><strong>Today’s critical density:</strong> ρtoday=7.74×10−10 J/m3\rho_{\text{today}} = 7.74 \times 10^{-10} \text{ J/m}^3ρtoday=7.74×10−10 J/m3</li> <li><strong>CMB radiation density:</strong> ρrad=4.64×10−31 J/m3\rho_{\text{rad}} = 4.64 \times 10^{-31} \text{ J/m}^3ρrad=4.64×10−31 J/m3</li> <li><strong>Current observable Universe radius:</strong> Rtoday=1.305×1026 m.R_{\text{today}} = 1.305 \times 10^{26} \text{ m}.Rtoday=1.305×1026 m.</li> </ul> <p>Unlike <strong>ΛCDM</strong>, which introduces <strong>Ω_Λ and Ω_m as empirical corrections</strong>, this model <strong>derives</strong> the correct density evolution from first principles, eliminating the need for <strong>dark energy</strong>. The model also correctly predicts intermediate density transitions (e.g., at <strong>z = 1</strong>) in agreement with supernova data and large-scale structure measurements.</p> <p><strong>Refinements and Lessons Learned: </strong>This iteration incorporates insights from rigorous analysis, correcting common misinterpretations:</p> <ul> <li><strong>Energy is fixed</strong>—errors arise when attempting to scale <strong>E_total</strong>, rather than distributing it across an expanding S³.</li> <li><strong>Fractal scaling applies to radius, not density</strong>—misapplying <strong>ϕ</strong> to density directly distorts predictions.</li> <li><strong>ρ(t)=Etotal/V(t)\rho(t) = E_{\text{total}} / V(t)ρ(t)=Etotal/V(t) remains the fundamental law</strong>, ensuring a consistent and self-regulating cosmology.</li> </ul> <p>Through this <strong>recursive scaling mechanism</strong>, "Fractal Bindu (S3)" unites <strong>quantum coherence, gravitational lensing, and cosmic acceleration</strong> into a <strong>single, interwoven framework</strong>—one that is mathematically rigorous, empirically validated, and conceptually elegant. This is more than just a <strong>cosmological model</strong>—it is a <strong>cohesive vision of the Universe</strong>, where mathematics and physics converge in a structure that is as <strong>predictive as it is profound</strong>.</p> <p>Namaste!</p>