The problem of cosmological acceleration (PCA) is usually considered in the framework of General Relativity and here the main uncertainty is how the background space is treated. In the approaches where it is flat, PCA is usually treated as a manifestation of dark energy and (as acknowledged in the literature) currently its nature is a mystery. On the other hand, if the background space is curved then a problem arises why the observed value of the cosmological constant is as is. Following the results of our publications, we show that the solution of PCA does not contain uncertainties because cosmological acceleration is an inevitable kinematical consequence of quantum theory in semiclassical approximation. In this approach, background space and its geometry (metric and connection) are not used and the cosmological constant problem does not arise.