Maciej Kowalczyk (IFT)

:In Loop Quantum Cosmology, one of the critical components is the so-called Thiemann regularization procedure, a technique imported from full Loop Quantum Gravity that allows one to define the quantum Hamiltonian constraint. However, this procedure is non-unique, leading to distinct mathematical formulations and, consequently, to different physical predictions. In this talk, I will present an investigation of how this regularization ambiguity affects the primordial power spectrum of cosmological perturbations, focusing on the three most studied regularization prescriptions in the literature. Initial conditions for perturbations are set at the quantum bounce, the replacement for the Big Bang singularity in Loop Quantum Cosmology, and corresponds to a vacuum state optimally adapted to the background dynamics. This state results from an asymptotic Hamiltonian diagonalization in the ultraviolet sector, which provides a non-oscillating power spectrum. For this so-called NO-AHD vacuum and by employing a suitable approximation to the perturbation equations around the bounce, it is possible to calculate the resulting primordial power spectrum for all considered regularizations in a full analytical manner. I will conclude my talk by comparing the results and discussing the main relevant distinction between the corresponding spectra.