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).
Highlights
The discovery of the cosmological repulsion has ignited a vast discussion on how this phenomenon should be interpreted
As follows from the above discussion, objects belonging to irreducible representations (IRs) of the de Sitter (dS) algebra can be treated as particles or antiparticles only if Poincare approximation works with a high accuracy
Since it is a reasonable requirement that dS theory should become the Poincare one at certain conditions, the above results show that in dS invariant theory only fermions can be elementary
Summary
The discovery of the cosmological repulsion (see e.g., [1,2]) has ignited a vast discussion on how this phenomenon should be interpreted. In Reference [5] we have proposed an interpretation that one IR of the dS algebra describes a particle and its antiparticle simultaneously. For deriving this result there is no need to involve spacetime background, Riemannian geometry, de Sitter quantum field theory (QFT), Lagrangians or other sophisticated methods. We tried to make the presentation self-contained and make it possible for readers to reproduce calculations without looking at other papers
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