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| 第一著者: | |
|---|---|
| フォーマット: | Recurso digital |
| 言語: | 英語 |
| 出版事項: |
Zenodo
2026
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| 主題: | |
| オンライン･アクセス: | https://doi.org/10.5281/zenodo.18249242 |
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目次:
- <p>This work presents a standalone, falsifiable prediction linking the cosmological constant <span><span>Λ\Lambda</span><span><span><span>Λ</span></span></span></span> to the fine-structure constant <span><span>α0\alpha_0</span><span><span><span><span>α</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span></span></span></span> through a geometric surface-projection relation.</p> <p>The proposed relation is</p> <p><span><span><span>ΩΛ≡Λc23H02=23N2α02,\Omega_\Lambda \equiv \frac{\Lambda c^2}{3H_0^2} = \frac{2}{3}N^2\alpha_0^2,</span><span><span><span>Ω<span><span><span><span><span><span>Λ</span></span></span><span></span></span></span></span></span><span>≡</span></span><span><span><span><span><span><span>3<span>H</span><span><span><span>0</span></span><span><span>2</span></span><span></span></span>Λ<span>c</span><span><span><span><span>2</span></span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span><span><span><span><span>32</span><span></span></span></span></span></span><span><span>N</span><span><span><span><span><span><span>2</span></span></span></span></span></span></span><span><span>α</span><span><span><span><span><span><span>0</span></span><span><span>2</span></span></span><span></span></span></span></span></span><span>,</span></span></span></span></span></p> <p>where <span><span>N=ln(1061)N=\ln(10^{61})</span><span><span><span>N</span><span>=</span></span><span><span>ln</span><span>(</span><span>1</span><span>0<span><span><span><span><span><span>61</span></span></span></span></span></span></span><span>)</span></span></span></span> represents the logarithmic hierarchy between Planck and cosmological scales.</p> <p>This yields the numerical prediction:</p> <p><span><span><span>ΩΛ,pred≈0.700,\Omega_{\Lambda,\mathrm{pred}} \approx 0.700,</span><span><span><span>Ω<span><span><span><span><span><span>Λ<span>,</span><span>pred</span></span></span></span><span></span></span></span></span></span><span>≈</span></span><span><span>0.700</span><span>,</span></span></span></span></span></p> <p>corresponding to</p> <p><span><span><span>Λpred≈1.12×10−52 m−2forH0≈67.4 km s−1 Mpc−1.\Lambda_{\mathrm{pred}} \approx 1.12\times10^{-52}\,\mathrm{m^{-2}} \quad \text{for} \quad H_0 \approx 67.4\,\mathrm{km\,s^{-1}\,Mpc^{-1}}.</span><span><span><span>Λ<span><span><span><span><span><span><span>pred</span></span></span></span><span></span></span></span></span></span><span>≈</span></span><span><span>1.12</span><span>×</span></span><span><span>1</span><span>0<span><span><span><span><span><span>−52</span></span></span></span></span></span></span><span><span>m</span><span><span><span><span><span><span>−<span>2</span></span></span></span></span></span></span></span><span><span>for</span></span><span><span>H</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>≈</span></span><span><span>67.4</span><span><span>km</span><span>s</span><span><span><span><span><span><span>−<span>1</span></span></span></span></span></span></span><span>Mp</span><span>c</span><span><span><span><span><span><span>−<span>1</span></span></span></span></span></span></span></span><span>.</span></span></span></span></span></p> <p>The relation is presented independently of any specific cosmological model, dark-energy field, or ΛCDM parameter fitting, and is formulated as a purely geometric predictive statement.</p> <p>The prediction is directly falsifiable by future precision measurements of <span><span>ΩΛ\Omega_\Lambda</span><span><span><span>Ω<span><span><span><span><span><span>Λ</span></span></span><span></span></span></span></span></span></span></span></span>, <span><span>α0\alpha_0</span><span><span><span><span>α</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span></span></span></span>, and <span><span>H0H_0</span><span><span><span><span>H</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span></span></span></span>. Any statistically significant deviation from the above relation would rule out the proposed correspondence.</p> <p>This record establishes priority for the proposed relation and provides a testable bridge between microphysical coupling and cosmological vacuum geometry.</p>