Can Quantum Geometrodynamics Complement General Relativity?
The properties of the universe as a whole are considered on the grounds of classical and quantum theories. For the maximally symmetric geometry, it is shown that the main equation of the quantum geometrodynamics is reduced to the non-linear Hamilton–Jacobi equation. In the semiclassical approximation, this non-linear equation is linearized and reduces to the Friedmann equation with the additional quantum source of gravity in the form of the stiff Zel’dovich matter. The semiclassical wave functions of the universe, in which different types of matter-energies dominate, are obtained. The cases of the domination of radiation, barotropic fluid, and new quantum matter-energy are discussed. The probability of the transition from the quantum state, where radiation dominates, into the state, in which a barotropic fluid in the form of a dust is dominant, is calculated.
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