Gravitational constant, cosmological constant and phases of quantum gravity based on the Wheeler-DeWitt equation

We re-examine the gravitational constant, cosmological constant and phases of quantum gravity based on the Wheeler-DeWitt equation, considering higher order contributions for the wave function in positive or negative (WKB) power expansions in terms of the Planck mass. It is found that, in an unstable state, the cosmological constant decreases with increasing (a) over tilde(mu), and the gravitational constant increases with increasing (a) over tilde(mu) for (a) over tilde(mu) less than or equal to (a) over tilde*(mu*) and decreases with increasing (a) over tilde(mu) for (a) over tilde(mu) greater than or equal to (a) over tilde*(mu*), where (a) over tilde(mu) is a renormalized cosmic-scale factor and (a) over tilde*(mu*) is a point in which the value of the gravitational constant becomes the maximum. This result may propose a new mechanism, in quantum gravity, which explain the facts that the observed cosmological constant is very small and gravitational forces ape remarkably weak in, atomic physics, by the old age of our expanding universe. We also briefly discuss the relation between our results and Dirac's large-number hypothesis.