Positive Cosmological Constant and Quantum Theory

TL;DR

This paper proposes that quantum theory should be based on Lie algebra symmetries rather than spacetime backgrounds, suggesting a positive cosmological constant naturally arises from de Sitter symmetry, eliminating the need for dark energy.

Contribution

It introduces a novel approach to quantum theory using Lie algebra symmetries, providing a new interpretation of the cosmological constant and particle properties in de Sitter space.

Findings

De Sitter algebra IRs differ from Poincare IRs, affecting particle-antiparticle relations.

Elementary particles are necessarily fermions; no neutral elementary particles exist.

Cosmological repulsion emerges as a kinematical consequence of de Sitter symmetry.

Abstract

We argue that quantum theory should proceed not from a spacetime background but from a Lie algebra, which is treated as a symmetry algebra. Then the fact that the cosmological constant is positive means not that the spacetime background is curved but that the de Sitter (dS) algebra as the symmetry algebra is more relevant than the Poincare or anti de Sitter ones. The physical interpretation of irreducible representations (IRs) of the dS algebra is considerably different from that for the other two algebras. One IR of the dS algebra splits into independent IRs for a particle and its antiparticle only when Poincare approximation works with a high accuracy. Only in this case additive quantum numbers such as electric, baryon and lepton charges are conserved, while at early stages of the Universe they could not be conserved. Another property of IRs of the dS algebra is that only fermions can be elementary and there can be no neutral elementary particles. The cosmological repulsion is a simple kinematical consequence of dS symmetry on quantum level when quasiclassical approximation is valid. Therefore the cosmological constant problem does not exist and there is no need to involve dark energy or other fields for explaining this phenomenon (in agreement with a similar conclusion by Bianchi and Rovelli).