In this seven-part paper, we show that gravitational waves (classical and quantum) produce the accelerated de Sitter expansion at the start and at the end of the cosmological evolution of the Universe. In these periods, the Universe contains no matte
r fields but contains classical and quantum metric fluctuations, i.e., it is filled with classical and quantum gravitational waves. In such evolution of the Universe, dominated by gravitational waves, the de Sitter state is the exact solution to the self-consistent equations for classical and quantum gravitational waves and background geometry for the empty space-time with FLRW metric. In both classical and quantum cases, this solution is of the instanton origin since it is obtained in the Euclidean space of imaginary time with the subsequent analytic continuation to real time. The cosmological acceleration from gravitational waves provides a transparent physical explanation to the coincidence, threshold and old cosmological constant paradoxes of dark energy avoiding recourse to the anthropic principle. The cosmological acceleration from virtual gravitons at the start of the Universe evolution produces inflation, which is consistent with the observational data on CMB anisotropy. Section 1 is devoted to cosmological acceleration from classical gravitational waves. Section 2 is devoted to the theory of virtual gravitons in the Universe. Section 3 is devoted to cosmological acceleration from virtual gravitons. Section 4 discusses the consistency of the theory with observational data on dark energy and inflation. The discussion of mechanism of acceleration and cosmological scenario are contained in Sections 5 and 6. Appendix contains the theory of stochastic nonlinear gravitational waves of arbitrary wavelength and amplitude in an isotropic Universe.
It is shown that the classical gravitational waves of super-horizon wavelengths are able to form the de Sitter accelerated expansion of the empty (with no matter fields) Universe. The contemporary Universe is about 70% empty and asymptotically is goi
ng to become completely empty, so the effect caused by emptiness should be already very noticeable. It could manifest itself as the dark energy.
It is shown that the de Sitter state is invariant with respect to Wick rotation. In imaginary time, super- horizon quantum and classical metric fluctuations of the empty FLRW space (with no matter fields) form a self-consistent de Sitter state. The i
nvariance with respect to Wick rotation suggests that this de Sitter state is formed also in the empty space of real time. At the start and by the end of its cosmological evolution the Universe is empty, so that the de Sitter expansion of the empty space can be the cause of inflation and dark energy. This scenario is consistent with the existing observational data
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.
We show that in imaginary time quantum metric fluctuations of empty space form a self-consistent de Sitter gravitational instanton that can be thought of as describing tunneling from nothing into de Sitter space of real time (no cosmological constant
or scalar fields are needed). For the first time, this mechanism is activated to give birth to a flat inflationary Universe. For the second time, it is turned on to complete the cosmological evolution after the energy density of matter drops below the threshold (the energy density of instantons). A cosmological expansion with dark energy takes over after the scale factor exceeds this threshold, which marks the birth of dark energy at a redshift $1+zapprox 1.3$ and provides a possible solution to the coincidence problem. The number of gravitons which tunneled into the Universe must be of the order of $10^{122}$ to create the observed value of the Hubble constant. This number has nothing to do with vacuum energy, which is a possible solution to the old cosmological constant problem. The emptying Universe should possibly complete its evolution by tunneling back to nothing. After that, the entire scenario is repeated, and it can happen endlessly.
