Snyder's Quantized Space-time and De Sitter Special Relativity

TL;DR

This paper explores the duality between Snyder's quantized space-time model and de Sitter-invariant special relativity, revealing a connection between Planck-scale physics and cosmological scales through local de Sitter invariance.

Contribution

It establishes a one-to-one correspondence between Snyder's model and de Sitter special relativity, highlighting a duality between Planck length and cosmological scale.

Findings

Physics at Planck length and cosmological scale are dual to each other.

Gravity with local de Sitter invariance is characterized by a tiny dimensionless coupling.

The duality suggests a unified perspective on quantum gravity and cosmology.

Abstract

There is a one-to-one correspondence between Snyder's model in de Sitter space of momenta and the \dS-invariant special relativity. This indicates that physics at the Planck length $\ell_P$ and the scale $R=3/\Lambda$ should be dual to each other and there is in-between gravity of local \dS-invariance characterized by a dimensionless coupling constant $g=\ell_P/R\sim 10^{-61}$.