  We propose a model of cosmological evolution of the early and late Universe
which is consistent with observational data and naturally explains the origin
of inflation and dark energy. We show that the de Sitter accelerated expansion
of the FLRW space with no matter fields (hereinafter, empty space) is its
natural state, and the model does not require either a scalar field or
cosmological constant or any other hypotheses. This is due to the fact that the
de Sitter state is an exact solution of the rigorous mathematically consistent
equations of one-loop quantum gravity for the empty FLRW space that are finite
off the mass shell. Space without matter fields is not empty, as it always has
the natural quantum fluctuations of the metric, i.e. gravitons. Therefore, the
empty (in this sense) space is filled with gravitons, which have the
backreaction effect on its evolution over time forming a self-consistent de
Sitter instanton leading to the exponentially accelerated expansion of the
Universe. At the start and the end of cosmological evolution, the Universe is
assumed to be empty, which explains the origin of inflation and dark energy.
This scenario leads to the prediction that the signs of the parameter 1+w
should be opposite in both cases, and this fact is consistent with
observations. The fluctuations of the number of gravitons lead to fluctuations
of their energy density which in turn leads to the observed CMB temperature
anisotropy of the order of 10^-5 and CMB polarization. In the frame of this
scenario, it is not a hypothetical scalar field that generates inflation and
relic gravitational waves but on the contrary, the gravitational waves
(gravitons) generate dark energy, inflation, CMB anisotropy and polarization.
