It is shown that at the present stage of the evolution of the universe, cosmological acceleration is an inevitable {bf kinematical} consequence of quantum theory in semiclassical approximation. Quantum theory does not involve such classical concepts as Minkowski or de Sitter spaces. In classical theory, when choosing Minkowski space, a vacuum catastrophe occurs, while when choosing de Sitter space, the value of the cosmological constant can be arbitrary. On the contrary, in quantum theory there are no uncertainties in view of the following: 1) the de Sitter algebra is the most general ten-dimensional Lie algebra; 2) the Poincare algebra is a special degenerate case of the de Sitter algebra in the limit $Rtoinfty$ where $R$ is the contraction parameter for the transition from the de Sitter to the Poincare algebra and $R$ has nothing to do with the radius of de Sitter space; 3) $R$ is fundamental to the same extent as $c$ and $hbar$: $c$ is the contraction parameter for the transition from the Poincare to the Galilean algebra and $hbar$ is the contraction parameter for the transition from quantum to classical theory; 4) as a consequence, the question (why the quantities $(c,hbar,R$) have the valueswhich they actually have) does not arise. The solution to the problem of cosmological acceleration follows from results on irreducible representations of the de Sitter algebra. This solution is free of uncertainties and does not involve dark energy, quintessence and other exotic mechanisms the physical meaning of which is a mystery.