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We study the imprint that certain quantization ambiguities may leave ineffective regimes of the hybrid loop quantum description of cosmologicalperturbations. More specifically, in the case of scalar perturbations weinvestigate how to reconstruct the Mukhanov-Sasaki field in the effectiveregime of Loop Quantum Cosmology, taking as starting point for the quantizationa canonical formulation in terms of other perturbative gauge invariants thatpossess different dynamics. This formulation of the quantum theory, in terms ofvariables other than the Mukhanov-Sasaki ones, is crucial to arrive at aquantum Hamiltonian with a good behavior, elluding the problems with illdefined Hamiltonian operators typical of quantum field theories. In thereconstruction of the Mukhanov-Sasaki field, we ask that the effectiveMukhanov-Sasaki equations adopt a similar form and display the same Hamiltonianstructure as the classical ones, a property that has been widely assumed inLoop Quantum Cosmology studies over the last decade. This condition actuallyrestricts the freedom inherent to certain quantization ambiguities. Once theseambiguities are removed, the reconstruction of the Mukhanov-Sasaki fieldnaturally identifies a set of positive-frequency solutions to the effectiveequations, and hence a choice of initial conditions for the perturbations. Ouranalysis constitutes an important and necessary test of the robustness ofstandard effective descriptions in Loop Quantum Cosmology, along with theirobservational predictions on the primordial power spectrum, taking into accountthat they should be the consequence of a more fundamental quantum theory with awell-defined Hamiltonian, in the spirit of Dirac's long-standing ideas.

Quantization ambiguities and the robustness of effective descriptions of primordial perturbations in hybrid Loop Quantum Cosmology