http://arxiv.org/abs/1509.02740
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of quasiclassical wave functions. The spacetime geometry is determined by the Robertson-Walker metric. It is shown that the main equation of the quantum geometrodynamics is reduced to the non-linear Hamilton-Jacobi equation. Its non-linearity is caused by a new source of the gravitational field, which has a purely quantum dynamical nature, and is additional to ordinary matter sources. In quasiclassical approximation, the non-linear equation of motion is linearized and reduces to the Friedmann equation with the additional quantum source of gravity (or anti-gravity) in the form of the stiff Zel’dovich matter. The semi-classical wave functions of the universe, in which different types of matter-energies dominate, are obtained. As examples, the cases of the domination of radiation, barotropic fluid, or new quantum matter-energy are discussed. The probability of the transition from the quantum state, where radiation dominates into the state, in which barotropic fluid in the form of dust is dominant, is calculated. In the era of matter-radiation equality, this probability has the same order of magnitude as the matter density contrast.
V. Kuzmichev and V. Kuzmichev
Thu, 10 Sep 15
43/67
Comments: 16 pages
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