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Tunneling Wave Function with Induced Gravity

A Tunneling wave function of the universe with induced gravity in the WKB approximation is discussed and using Vilenkin's boundary condition we obtain the probability density for the scale factor α at a given value of the scalar field cursive φ. It is shown that when the universe spontaneously nucleates, the minimum value of the scale factor of the classical universe is of the order of Planck length.