Dark Energy and Inflation from Gravitational Waves

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 matter 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.Comment: 51 pages; This paper belongs to the Special Issue "Progress in Cosmology in the Centenary of the 1917 Einstein Paper", Universe 2017, 3(4), 72; With the permission of the journal "Universe

Quantum gravity in Heisenberg representation and self-consistent theory of gravitons in macroscopic spacetime

The first mathematically consistent exact equations of quantum gravity in the Heisenberg representation and Hamilton gauge are obtained. It is shown that the path integral over the canonical variables in the Hamilton gauge is mathematically equivalent to the operator equations of quantum theory of gravity with canonical rules of quantization of the gravitational and ghost fields. In its operator formulation, the theory can be used to calculate the graviton S-matrix as well as to describe the quantum evolution of macroscopic system of gravitons in the non-stationary Universe or in the vicinity of relativistic objects. In the S-matrix case, the standard results are obtained. For problems of the second type, the original Heisenberg equations of quantum gravity are converted to a self-consistent system of equations for the metric of the macroscopic spacetime and Heisenberg operators of quantum fields. It is shown that conditions of the compatibility and internal consistency of this system of equations are performed without restrictions on the amplitude and wavelength of gravitons and ghosts. The status of ghost fields in the various formulations of quantum theory of gravity is discussed.Comment: 15 pages; v2: Expanded explanation of the reasons why the vast majority of papers on the quantum theory of gravitons published in 1977-2008 is erroneou

The Oort cloud

Views of the large-scale structure of the solar system, consisting of the Sun, the nine planets and their satellites, changed when Oort demonstrated that a gigantic cloud of comets (the Oort cloud) is located on the periphery of the solar system. The following subject areas are covered: (1) the Oort cloud's mass; (2) Hill's cloud mass; (3) angular momentum distribution in the solar system; and (4) the cometary cloud around other stars

Cosmological Acceleration from Virtual Gravitons

Intrinsic properties of the space itself and quantum fluctuations of its geometry are sufficient to provide a mechanism for the acceleration of cosmological expansion (dark energy effect). Applying Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy approach to self-consistent equations of one-loop quantum gravity, we found exact solutions that yield acceleration. The permanent creation and annihilation of virtual gravitons is not in exact balance because of the expansion of the Universe. The excess energy comes from the spontaneous process of graviton creation and is trapped by the background. It provides the macroscopic quantum effect of cosmic acceleration.Comment: 6 pages, REVTeX

Dark energy from instantons

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 $1+z\approx 1.3$ 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.Comment: 11 two-column pages, 1 figure, V2 is updated pre-publication version. The title is changed. Section 4 (Birth of Dark Energy) is extended. Misprints are fixe