Further improvements in the understanding of LQC

Abstract

Loop Quantum Cosmology provides a successful quantization of isotropic and homogeneous flat universes with a massless, homogeneous scalar field as the matter content. Here, we propose a new ordering for the Hamiltonian constraint operator that facilitates the quantization of this model and makes the physical consequences much more transparent. In particular, our constraint is such that, in the gravitational sector, the zero volume state decouples, allowing us to get rid of the cosmological singularity already at a kinematical level, as well as to introduce a consistent densitization procedure for the constraint. Furthermore, the typical discretization of the spatial volume is achieved in superselection sectors which prove to be most suitable, with support on semilattices and where the basic functions that codify all the relevant information about the geometry have the expected Wheeler-DeWitt limit of standing waves. Thanks to these properties, we can demonstrate that the quantum bounce is generic for any physical state and superselection sector.