Reflected waves and quantum gravity

In the context of canonical quantum gravity, we consider the effects of a nonstandard 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, nonperturbative, approach is used to study the evolution. Finally, a simplified application is fully illustrated and commented.