de Sitter special relativity

TL;DR

This paper introduces de Sitter special relativity, a theory adapting special relativity to include a non-zero cosmological constant, resulting in modified spacetime structure, energy-momentum relations, and potential experimental implications.

Contribution

It formulates a de Sitter invariant special relativity, extending the Poincaré group framework to incorporate a cosmological constant and exploring its physical and causal consequences.

Findings

De Sitter special relativity retains spacetime homogeneity.

Modified energy and momentum relations are derived.

Potential experimental and causal implications are discussed.

Abstract

A special relativity based on the de Sitter group is introduced, which is the theory that might hold up in the presence of a non-vanishing cosmological constant. Like ordinary special relativity, it retains the quotient character of spacetime, and a notion of homogeneity. As a consequence, the underlying spacetime will be a de Sitter spacetime, whose associated kinematics will differ from that of ordinary special relativity. The corresponding modified notions of energy and momentum are obtained, and the exact relationship between them, which is invariant under a re-scaling of the involved quantities, explicitly exhibited. Since the de Sitter group can be considered a particular deformation of the Poincar\'e group, this theory turns out to be a specific kind of deformed (or doubly) special relativity. Some experimental consequences, as well as the causal structure of spacetime--modified by the presence of the de Sitter horizon--are briefly discussed.