Starobinsky potential and power suppression in hybrid Loop Quantum Cosmology

Abstract

We study the effect on the primordial tensor power spectrum of varying the number of e-folds during slow-roll inflation in Loop Quantum Cosmology with a Starobinsky potential. Using the hybrid quantization approach, we derive the effective mass governing tensor mode evolution. The choice of vacuum state is crucial, especially since the preinflationary phase predicted by Loop Quantum Cosmology invalidates the choice of the Bunch-Davies state as the preferred vacuum. We adopt a choice which is optimally adapted to the dynamics, so that it provides a non-oscillating (NO) spectrum free of spurious contributions, and permits an asymptotic Hamiltonian diagonalization (AHD) of the perturbations. For this so-called NO-AHD vacuum, we compute the power spectrum using both analytic approximations and numerical integration. Our results confirm the accuracy of our approximations in a wide range of situations, including short- and long-lived inflationary scenarios. The primordial power spectrum exhibits a characteristic cutoff on a wavenumber scale determined primarily by the background dynamics around the bounce that replaces the big bang in Loop Quantum Cosmology.