Cosmological acceleration from a scalar field and classical and quantum gravitational waves (Inflation and dark energy)

We show that, on the average, a homogeneous and isotropic scalar field and, on the average, homogeneous and isotropic ensembles of classical and quantum gravitational waves generate the de Sitter expansion of empty (with no matter) space-time. At the start and by the end of its cosmological evolution, the Universe is empty. The contemporary Universe is about 70% empty, so the effect of cosmological acceleration should be very noticeable. One can assume that itmanifests itself as dark energy. At the start of the cosmological evolution, before the firstmatter was born, the Universe was also empty. The cosmological acceleration of such empty space-time can manifests itself as inflation. To get the de Sitter accelerated expansion of empty space-time under influence of scalar fields and classical and quantum gravitational waves, one needs to make a mandatory Wick rotation, i.e., one needs to make a transition to Euclidean space of imaginary time. One can assume that the very existence of inflation and dark energy could be considered as a possible observable evidence for the fact that time by its nature could be a complex value which manifests itself precisely at the start and by the end of the evolution of the Universe, i.e., in those periods when the Universe is empty (or nearly empty).