Doubly special relativity in de Sitter spacetime

TL;DR

This paper extends Doubly Special Relativity to de Sitter spacetime, introducing a model with three observer-independent scales and a noncommutative position space, revealing a duality between positions and momenta.

Contribution

It generalizes Doubly Special Relativity to curved spacetime with three invariant scales and explores a duality symmetry in the model.

Findings

Model incorporates three observer-independent scales: c, α, κ.

Realizes a noncommutative position space.

Exhibits a duality between positions and momenta.

Abstract

We discuss the generalization of Doubly Special Relativity to a curved de Sitter background. The model has three observer-independent scales, the velocity of light $c$, the radius of curvature of the geometry $\alpha$, and the Planck energy $\kappa$, and can be realized in a noncommutative position space. It is possible to construct a model exhibiting a duality for the interchange of positions and momenta together with the exchange of $\alpha$ and $\kappa$.