Analytic and numerical study of scalar perturbations in loop quantum cosmology

The possibility that quantum geometry effects may alleviate the apparent tensions existing at large angular scales in the observations of the cosmic microwave background explains the increasing interest in considering primordial perturbations within the framework of loop quantum cosmology. In this framework, a number of approximations have been suggested to simplify the study of perturbations and derive analytic expressions for the power spectra. This study requires a new choice of vacuum state that takes into account the preinflationary background geometry, a choice for which we adopt the so-called nonoscillating with asymptotic Hamiltonian diagonalization (NO-AHD) prescription. Here, we apply the aforementioned approximations to the investigation of scalar perturbations. We discuss two approaches to the quantization of perturbations in loop quantum cosmology, namely the hybrid and the dressed metric approaches. We improve previous approximations by including slow-roll corrections in the inflationary era. Moreover, for the first time in the literature of the NO-AHD prescription, we compute numerically the primordial power spectra for the two considered approaches, and show that the analytic estimations are remarkably accurate for all observable modes. We also discuss the similarities and differences between the spectra obtained with those two approaches.