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

Han-Ying Guo·Chao-Guang Huang·Yu Tian·Hong-Tu Wu·Zhan Xu·Bin Zhou
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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 $\ell_P$, $R\simeq (3/Λ)^{1/2}$ should be a fundamental constant. They lead to a dimensionless constant $g{\sim\ell_PR^{-1}}=(G\hbar c^{-3}Λ/3)^{1/2}\sim 10^{-61}$. 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.

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Han-Ying Guo, Chao-Guang Huang, Yu Tian, Hong-Tu Wu, Zhan Xu, Bin Zhou. 2007-08-14. Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity. https://doi.org/10.1088/0264-9381%2F24%2F16%2F004

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