  Recently, a lot of attention has been paid to the modifications of the power
spectrum of primordial fluctuations caused by quantum cosmology effects. The
origin of these modifications are corrections to the Mukhanov-Sasaki equations
that govern the propagation of the primeval cosmological perturbations. The
specific form of these corrections depends on a series of details of the
quantization approach and of the prescription followed to implement it.
Generally, nonetheless, the complexity of the theoretical quantum formulation
is simplified in practice appealing to a semiclassical or effective
approximation, in order to perform concrete numerical computations. In this
work, we introduce technical tools and design a procedure to deal with these
quantum corrections beyond the most direct approximations employed so far in
the literature. In particular, by introducing an interaction picture, we
extract the quantum dynamics of the homogeneous geometry in absence of scalar
field potential and inhomogeneities, dynamics that has been intensively studied
and that can be integrated. The rest of our analysis focuses on the interaction
evolution, putting forward methods to cope with it. The ultimate aim is to
develop treatments that increase our ability to discriminate between the
predictions of different quantization proposals for cosmological perturbations.
