Conserved quantities for the Sitter particles$^*$

TL;DR

This paper explores conserved quantities in de Sitter space to better understand the physics of particles in a universe with a positive cosmological constant, emphasizing intrinsic characterizations independent of coordinate choices.

Contribution

It introduces a method to define conserved quantities for free particles in de Sitter space in an intrinsic, coordinate-independent manner, relevant for classical scattering and decay processes.

Findings

Conserved quantities can be characterized intrinsically in de Sitter space.

This approach facilitates the analysis of classical particle interactions.

It provides a foundation for understanding particle dynamics in an accelerating universe.

Abstract

Recent observations of the luminosity-red shift relation of distant type Ia supernovae established the fact that the expansion of the universe is accelerated. This is interpreted by saying that there exists some kind of agent (called dark energy), which exerts an overall repulsive effect on ordinary matter. Dark energy contributes today in the amount of about 73 % to the total energy content of the universe, and its spatial distribution is compatible with perfect uniformity. The simplest possible explanation for dark energy is to assume that it is just a universal constant, the so called cosmological constant. This would mean that the background arena for all natural phenomena, once all physical matter-energy has been ideally removed, is the de Sitter space time. Thus, the Poincar\'e group should be replaced by the de Sitter group, and one is naturally led to a reformulation of the theory of special relativity on these grounds. The absence of a privileged class of equivalent frames (inertial frames) suggests that, in de Sitter relativity it would be desirable, to characterize significant physical quantities in an intrinsic way, namely in a manner independent of the choice of any particular coordinate patch. In this talk we would like to show how this can be accomplished for any set of independent conserved quantities along the geodesic motion of a free de Sitter particle. These quantities allow for a natural discussion of classical pointlike scattering and decay processes.