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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19556850 |
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| author | Lee, Howard S. |
| author_facet | Lee, Howard S. |
| contents | <p>The radial acceleration relation scale a0 and the interpolation function ν(x) = 1/(1− e − √ x ) are derived from the thermal boundary physics of a de Sitter shell, with no adjustable parameters. The scale is fixed by the type-A conformal anomaly coefficient; the functional form is fixed by the KMS boundary kernel independently of the anomaly. For ∆a = aSM = 1991/720 (the Standard Model anomaly coefficient) and the Planck H0: a0 = cH0 2∆a · ζ(2∆a + 1)/ζ(2∆a) = 1.199 × 10−10 m s−2 , matching the observed central value a obs 0 = 1.20 ± 0.02 (stat) × 10−10 m s−2 [1] at the 0.08% level. Both results follow from a single worldtube operator L whose spectrum is fixed by the Euler-projected anomaly effective action on the de Sitter shell. The heat sector of L gives the scale (Theorem 1): an anomaly-weighted Bose–Einstein spectrum, calibrated at the Unruh/Gibbons–Hawking crossover, determines a0. The Poisson sector gives the interpolation law (Theorem 2): the KMS boundary kernel of L 1/2 on the thermal circle, evaluated at coincidence and normalised by the vacuum kernel, gives ν(x). The √ x is the linear conformal invariant of the boundary worldtube, where the bulk quadratic invariant x = e2ϕˆ reduces to eϕˆ = √ x; the Dirichlet-to-Neumann map confirms this independently. The physical inputs are the thermal framework (the semiclassical path integral over shell configurations, weighted by the Euler-projected anomaly effective action at the de Sitter KMS temperature) and the Standard Model field content; the domain of validity is restricted to circular outer orbits in the probe limit.</p> <p>Keywords: radial acceleration relation; conformal anomaly; entanglement entropy; de Sitter thermodynamics; equilibrium partition function</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19556850 |
| institution | Zenodo |
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| publishDate | 2026 |
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| spellingShingle | The Radial Acceleration Relation from de Sitter Thermodynamics Lee, Howard S. <p>The radial acceleration relation scale a0 and the interpolation function ν(x) = 1/(1− e − √ x ) are derived from the thermal boundary physics of a de Sitter shell, with no adjustable parameters. The scale is fixed by the type-A conformal anomaly coefficient; the functional form is fixed by the KMS boundary kernel independently of the anomaly. For ∆a = aSM = 1991/720 (the Standard Model anomaly coefficient) and the Planck H0: a0 = cH0 2∆a · ζ(2∆a + 1)/ζ(2∆a) = 1.199 × 10−10 m s−2 , matching the observed central value a obs 0 = 1.20 ± 0.02 (stat) × 10−10 m s−2 [1] at the 0.08% level. Both results follow from a single worldtube operator L whose spectrum is fixed by the Euler-projected anomaly effective action on the de Sitter shell. The heat sector of L gives the scale (Theorem 1): an anomaly-weighted Bose–Einstein spectrum, calibrated at the Unruh/Gibbons–Hawking crossover, determines a0. The Poisson sector gives the interpolation law (Theorem 2): the KMS boundary kernel of L 1/2 on the thermal circle, evaluated at coincidence and normalised by the vacuum kernel, gives ν(x). The √ x is the linear conformal invariant of the boundary worldtube, where the bulk quadratic invariant x = e2ϕˆ reduces to eϕˆ = √ x; the Dirichlet-to-Neumann map confirms this independently. The physical inputs are the thermal framework (the semiclassical path integral over shell configurations, weighted by the Euler-projected anomaly effective action at the de Sitter KMS temperature) and the Standard Model field content; the domain of validity is restricted to circular outer orbits in the probe limit.</p> <p>Keywords: radial acceleration relation; conformal anomaly; entanglement entropy; de Sitter thermodynamics; equilibrium partition function</p> |
| title | The Radial Acceleration Relation from de Sitter Thermodynamics |
| url | https://doi.org/10.5281/zenodo.19556850 |