Spontaneous creation of the universe from nothing
An interesting idea is that the universe could be spontaneously created from nothingbut no rigorousproof has been given. In this paperwe present such a proof based on the analytic solutions of the Wheeler-DeWitt equation (WDWE). Explicit solutions of the WDWE for the special operator ordering factorp= -2 (or 4) show thatonce a small true vacuum bubble is created by quantum fluctuations of themetastable false vacuumit can expand exponentially no matter whether the bubble is closed,flat,or open.The exponential expansion will end when the bubble becomes large and thus the early universe appears.With the de Broglie-Bohm quantum trajectory theorywe show explicitly that it is the quantum potentialthat plays the role of the cosmological constant and provides the power for the exponential expansion of thetrue vacuum bubble. So it is clear that the birth of the early universe completely depends on the quantum nature of the theory.