Constraining quantization ambiguities from effective descriptions of cosmological perturbations in hybrid Loop Quantum Cosmology
Beatriz Elizaga Navascués, Guillermo Antonio Mena Marugán · arXiv (Cornell University) · 2021
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.