  We argue that fundamental objects in particle theory are not elementary
particles and antiparticles but objects described by irreducible
representations (IRs) of the de Sitter (dS) algebra. One might ask why, then,
experimental data give the impression that particles and antiparticles are
fundamental and there are conserved additive quantum numbers (electric charge,
baryon quantum number and others). The matter is that, at the present stage of
the universe, the contraction parameter $R$ from the dS to the Poincare algebra
is very large and, in the formal limit $R\to\infty$, one IR of the dS algebra
splits into two IRs of the Poincare algebra corresponding to a particle and its
antiparticle with the same masses. The problem why the quantities $(c,\hbar,R)$
are as are does not arise because they are contraction parameters for
transitions from more general Lie algebras to less general ones. Then the
baryon asymmetry of the universe problem does not arise. At the present stage
of the universe, the phenomenon of cosmological acceleration (PCA) is described
without uncertainties as an inevitable {\it kinematical} consequence of quantum
theory in semiclassical approximation. In particular, it is not necessary to
involve dark energy the physical meaning of which is a mystery. In our
approach, background space and its geometry are not used and $R$ has nothing to
do with the radius of dS space. In semiclassical approximation, the results for
PCA are the same as in General Relativity if $\Lambda=3/R^2$, i.e., $\Lambda>0$
and there is no freedom in choosing the value of $\Lambda$.
