Research On Some Problems In The Quantum Origin Of The Universe

The chapters 1 and 2 in the thesis give the background knowledge and the developing procedure of the cosmological theory, summarize the view-points in the cosmological models such as standard inflationary cosmological model, high-temperature revised inflationary cosmological model, chaotic inflationary cosmological model, supermmetric inflationary cosmological model. The problem how the universe started can be solved by quantum cosmologyical wave function that is satisfied with cosmological Wheeler-DeWitt eqation. Cosmological wave function also satisfies momentum restraining equation. Momentum restraining eqation and Wheeler-DeWitt equation are quantum geometrical dynamical equation. Zero energy Schr?dinger equation H Ψ=0 can be decomposed into momentum restraining eqation and Wheeler-DeWitt equation. The universe can be created from zero by going through tunnel. The big bang occurs after the tunneling. The theory that cosmological quantum state can be described by the route integral can explain the origin of the universe. The third chapter studies the solution of the Wheeler-DeWitt equation, the tunneling effect and the potential well effect, and gives the discussion of the solution. The "twice loosed shoe"method tries to discuss Wheeler-DeWitt equation by fixing the cosmological scalar factor a and the scalar field Φin turn. This method can conquer the great field difficulty caused by only considering the tunnelling effect of the birth of the quantum universe. The potential well effect of the field Φprovides the probability truncation. The potential well effect compresses the field Φso that it overcomes the great field difficult. This thesis connects the tunnelling effect of the cosmological scalar factor a and the quantum potential well of the scalar field Φ. It provides the model of the cosmological birth based on the Wheeler-DeWitt equation. Because the universe may originate from the decay of the scalar field Φ, the early cosmological radius depends on the scalar field Φ. So we can assume a= α)0Φ~β.The cosmological scalar factor a and the scalar field Φcan change at the same time. It overcome the defect that leads to a and Φseparating man-madely in the "twice loosing shoe"means of first fixing Φ, namely ording (?)Ψ/(?)Φ=0 ,and then fixing a, namely ording (?)Ψ/ (?)a =0. Using the method of solving Wheeler-DeWitt equation, we obtain the probability distribution of the universe's birth. The scalar field Φdiminishes with the augmentation of the cosmological scalar factor a, the universe is borned from the inflation, i.e. the extremely quantum expansion, there may be the tiny quantum stir left, and it enters the classical big bang stage. The fourth chapter obtains the solution of the Wheeler-DeWitt equation of the restriction system in Friedmann cosmology, and obtains the solutions for the different forms of V( ? ),...