Abstract
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.
Highlights
In the period of 2008–2017, we published a series of papers [1,2,3,4,5,6,7] on the cosmological acceleration generated by classical and quantum gravitational waves of the super-horizon wavelengths
There is no self-consistent solution to the problem of backreaction of classical gravitational waves in the empty space in real time
The transition to the Euclidian space of imaginary time produces the self-consistent de Sitter solution in such a space. This de Sitter solution in imaginary time was analytically continued into the Lorentzian space of real time
Summary
In Appendix A, we obtained a set of exact self-consistent equations describing an ensemble of stochastic nonlinear classical gravitational waves of arbitrary amplitudes and wavelengths isotropic on average. We use an approximation, in which these equations describe the backreaction of linear waves that affects the background metric, which in turn affects the state of gravitational waves. This means that the interaction of gravitational waves is taken into account only through self-consistent background gravitational fields. In this approximation, superhorizon waves form the de Sitter state in the empty (with no matter fields) space-time with FLRW metric. This number has nothing to do with vacuum energy, which is a possible solution to the “old cosmology constant problem”
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