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

References in corpus (1)

• Quantum gravity in terms of topological observables

Cited by in corpus (3)

• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
• On Torsion-free Vacuum Solutions of the Model of de Sitter Gauge Theory of Gravity
• From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality