Doubly special relativity in de Sitter spacetime

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 $\kappa$.

18 pages, plain TeX

References in corpus (8)

• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Triply Special Relativity
• de Sitter special relativity
• Special Relativity in the 21${}^{\mathrm{st}}$ century
• The Free Particle in Deformed Special Relativity
• Doubly special relativity and translation invariance
• Interplay between curvature and Planck-scale effects in astrophysics and cosmology
• Lifetime of flying particles in canonical Doubly Special Relativity

Cited by in corpus (20)

• Classical and quantum mechanics of the nonrelativistic Snyder model
• Self-sustained wormholes in modified dispersion relations
• Investigation of Unruh temperature of Black holes by using of EGUP formalism
• Classical dynamics on curved Snyder space
• Non-commutative Geometry from Perturbative Quantum Gravity
• Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space
• Kinematics of particles with quantum de Sitter symmetries
• Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity
• Symmetries of Snyder--de Sitter space and relativistic particle dynamics
• Snyder-de Sitter model from two-time physics
• Generalizations of Snyder model to curved spaces
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Noncommutative Yang model and its generalizations
• Graphene in curved Snyder space
• Relativistic deformed kinematics: from flat to curved spacetimes
• On the rest and flat limits of the scalar modes on the de Sitter spacetime
• Five-Dimensional Mechanics as the Starting Point for the Magueijo-Smolin Doubly Special Relativity
• Three dimensional DKP oscillator in a curved Snyder space
• 5-Dimensional $SO(1,4)$-Invariant Action as an Origin to the Magueijo-Smolin Doubly Special Relativity Proposal
• Symplectic realization of generalized Snyder-Poisson algebra