  We study the imprint that certain quantization ambiguities may leave in
effective regimes of the hybrid loop quantum description of cosmological
perturbations. More specifically, in the case of scalar perturbations we
investigate how to reconstruct the Mukhanov-Sasaki field in the effective
regime of Loop Quantum Cosmology, taking as starting point for the quantization
a canonical formulation in terms of other perturbative gauge invariants that
possess different dynamics. In this reconstruction, we impose that the
effective Mukhanov-Sasaki equations adopt a similar form and display the same
Hamiltonian structure as the classical ones. The restrictions that result from
this condition are used to constrain ambiguities that arise in the quantization
process. Such ambiguities affect the quantum representation of certain Poisson
brackets that appear in the Hamiltonian constraint of the system, and their
effects on the Mukhanov-Sasaki equations reflect the different Hamiltonian
evolution of the homogeneous cosmological background that is found in the
effective regime of Loop Quantum Cosmology compared to the classical
trajectories. Our analysis constitutes an important step to trascend the
effective description and put forward quantization prescriptions with
satisfactory physical results.
