The phenomenon of the cosmological acceleration discovered in 1998 is usually explained as a manifestation of a hypothetical field called dark energy which is believed to contain more than 70% of the energy of the Universe. This explanation is based on the assumption that empty space-time background should be flat and hence a nonzero curvature of the background is a manifestation of a hidden matter. We argue that quantum theory should proceed not from space-time background but from a symmetry algebra. Then the cosmological acceleration can be easily and naturally explained from first principles of quantum theory without involving empty space-time background, dark energy and other artificial notions. We do not assume that the reader is an expert in the given field and the content of the paper can be understood by a wide audience of physicists.