Further improvements in the understanding of isotropic loop quantum cosmology

M. Martín-Benito, G. A. Mena Marugán and J. Olmedo

Loop Quantum Gravity (LQG) is a solid candidate to make general relativity compatible with quantum mechanics. The quantization of symmetry reduced models following the lines of LQG is known as Loop Quantum Cosmology (LQC). A paradigmatic model in LQC is the flat Friedman-Robertson-Walker spacetime coupled to a massless scalar field. Its quantization à la loop has provided remarkable results, e.g. the replacement of the initial singularity (big bang) by a quantum bounce if one considers appropriate semiclassical states. Even though this model has recieved considerable attention in the context of LQC, there exist some fundamental aspects of its quantization that need further exploration. These aspects are investigated in this talk. On one hand, we propose a rigorous densitization procedure for the Hamiltonian Constraint of the system at the quantum level. On the other hand, we introduce a proposal which leads to superselection sectors that are as simple as possible and possess optimal physical properties. Thanks to these properties, the Wheeler-DeWitt limit of the theory turns out to be uniquely defined in each superselection sector. More importantly, we prove that the quantum bounce is a general feature of the model, independently of the considered physical state or the particular superselection sector that one chooses.