Quantum cosmological model of the inflationary universe

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Abstract
A quantum cosmological model of the inflationary universe is investigated by solving the Wheeler-DeWitt equation. We consider a model with a minimally coupled scalar field, the potential of which is a simple double well. By applying the boundary condition of ‘‘no boundary,’’ we calculate the wave function of our model universe. We find that in a certain parameter range a big peak is formed near the maximum of the double-well potential of the scalar field, accompanied by a recession of the exponential behavior of the wave function. We show that this peak can be consistently interpreted as representing a high density of classical paths of generalized oscillating universes, and as a consequence of the constructive interference of quantum states corresponding to these classical paths by the WKB approximation. The cosmological scenario with nonvanishing, nearly critical ‘‘velocity’’ of the vacuum expectation value in the early universe, which is suggested by the behavior of the wave function, is discussed.

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