Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity

Abstract

Between Snyder's quantized space-time model in de Sitter space of momenta and the \dS special relativity on \dS-spacetime of radius $R$ with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with Planck length ${\ell }_P$, $R\simeq (3/\Lambda {)}^{1/2}$ should be a fundamental constant. They lead to a dimensionless constant $g\sim {\ell }_P{R}^{-1}=(G\hslash c^{-3}\Lambda /3{)}^{1/2}\sim 10^{-61}$. These indicate that physics at these two scales should be dual to each other and there is in-between gravity of local \dS-invariance characterized by $g$. A simple model of \dS-gravity with a gauge-like action on umbilical manifolds may show these characters. It can pass the observation tests and support the duality.

32 pages

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• de Sitter special relativity
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• Cosmological Solutions with Torsion in a Model of de Sitter Gauge Theory of Gravity
• On the spacetime connecting two aeons in conformal cyclic cosmology
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• de Sitter geodesics: reappraising the notion of motion
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• Quantum Discrete Levels of the Universe from the Early Trans-Planckian Vacuum to the Late Dark Energy
• De Sitter spacetimes with torsion in the model of dS gauge theory of gravity
• Schwarzschild-de Sitter Metric and Inertial Beltrami Coordinates
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• Geometries for Possible Kinematics
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• On Torsion-free Vacuum Solutions of the Model of de Sitter Gauge Theory of Gravity (II)
• On determination of the geometric cosmological constant from the OPERA experiment of superluminal neutrinos
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