de Sitter geodesics: reappraising the notion of motion

TL;DR

This paper reexamines geodesics in de Sitter spacetime, introducing a new family of trajectories that incorporate conformal transformations, potentially impacting high-energy physics where conformal symmetry is relevant.

Contribution

It proposes a novel family of geodesics in de Sitter spacetime that connect any two points by considering conformal transformations, expanding the traditional notion of motion.

Findings

New geodesics connect all points in de Sitter spacetime.

The new trajectories combine translations and conformal transformations.

Potential relevance at very-high energies where conformal symmetry is significant.

Abstract

The de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are points in de Sitter spacetime which cannot be joined to each other by any one of these geodesics. By taking into account the appropriate transitivity properties in the variational principle, a new family of maximizing trajectories is obtained, whose members are able to connect any two points of the de Sitter spacetime. These geodesics introduce a new notion of motion, given by a combination of translations and proper conformal transformations, which may possibly become important at very-high energies, where conformal symmetry plays a significant role.