The contraction of the representations of the group $SO(4,1)$ and cosmological interpretation

TL;DR

This paper studies how representations of the de Sitter group contract to those of the Poincaré group, providing a quantum perspective on dark matter and dark energy phenomena.

Contribution

It demonstrates the contraction process of de Sitter group representations to Poincaré group representations, linking group theory to cosmological phenomena.

Findings

Contraction yields a sum of Poincaré representations with different rest mass signs.

Provides a quantum group-theoretic interpretation of dark matter and dark energy.

Connects mathematical representation theory with cosmological observations.

Abstract

We consider the operation of contraction of unitary irreducible representations of the de Sitter group $ SO(4,1) $. It is shown that a direct sum of unitary irreducible representations of the Poincar\'{e} group with different signs of the rest mass is obtained as a result of contraction. The results obtained are used to interpret the phenomena of "dark matter" and "dark energy" in terms of the elementary quantum systems of de Sitter's world.