An interesting idea is that the universe could be spontaneously created from
nothing, but no rigorous proof has been given. In this paper, we 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 factor p=-2
(or 4) show that, once a small true vacuum bubble is created by quantum
fluctuations of the metastable false vacuum, it 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 theory, we show explicitly that it
is the quantum potential that plays the role of the cosmological constant and
provides the power for the exponential expansion of the true vacuum bubble. So
it is clear that the birth of the early universe completely depends on the
quantum nature of the theory.Comment: The problem of singularity can be avoided naturally as the universe
can be spontaneously created from nothin
In this paper, we study the physical meaning of the wavefunction of the
universe. With the continuity equation derived from the Wheeler-DeWitt (WDW)
equation in the minisuperspace model, we show that the quantity
$\rho(a)=|\psi(a)|^2$ for the universe is inversely proportional to the Hubble
parameter of the universe. Thus, $\rho(a)$ represents the probability density
of the universe staying in the state $a$ during its evolution, which we call
the dynamical interpretation of the wavefunction of the universe. We
demonstrate that the dynamical interpretation can predict the evolution laws of
the universe in the classical limit as those given by the Friedmann equation.
Furthermore, we show that the value of the operator ordering factor $p$ in the
WDW equation can be determined to be $p=-2$
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