  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).
