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

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

2007-03-14

arxiv.org/abs/gr-qc/0703078v2

Class.Quant.Grav.24:4009-4036,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

32 pages

Scientific paper

10.1088/0264-9381/24/16/004

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 $g{\sim\ell_PR^{-1}}=(G\hbar c^{-3}\Lambda/3)^{1/2}\sim 10^{-61}$. 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.

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