In the context of canonical quantum gravity, we consider the effects of a
    non-standard expression for the gravitational wave function on the evolution of
    inflationary perturbations. Such an expression and its effects may be generated
    by a sudden variation in the (nearly constant) inflaton potential. The
    resulting primordial spectra, up to the leading order, are affected in the
    short and in the long wavelength regime, where an oscillatory behavior with a
    non-negligible amplitude is superimposed on the standard semiclassical result.
    Moreover, a novel, non-perturbative, approach is used to study the evolution.
    Finally, a simplified application is fully illustrated and commented.

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