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The semiclassical approach to quantum gravity would yield the Schrödinger formalism for the wave function of metric perturbations or gravitons plus quantum gravity correcting terms in pure gravity; thus, in the inflationary scenario, we should expect correcting effects to the relic graviton (Zel'dovich) spectrum of the order of (λ/m 2 P l ). These, on the other hand, could possibly be measured in a future experiment.

Upon using some special example in the homogeneous cosmological model we develop the idea that, as a result of the arbitrariness of the factor ordering in Wheeler-DeWitt equation, gauge phases can not, in general, being completely removed from the wave functional in quantum gravity. The latter may be conveniently described by means of a remnant complex term in WDW equation depending on the factor ordering. Taking this equation for granted we can obtain WKB complex solutions and, therefore, we should be able to derive a semiclassical time parameter for the Schrödinger equation corresponding to matter fields in a given classical curved space. 4.60.+n,03.65Bz,04.20.Fy

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