Bouncing universes analytic and effective dynamics in reduced-symmetry models of loop quantum cosmology

The Singularity Problem in classical General Relativity and the need of a quantum theory for the gravitational field are two of the reasons that brought to the formulation of Loop Quantum Gravity, one of the most accredited theories of Quantum Gravity. In this work we analyze the main features of the theory, from the Kinematical Hilbert space to the physical one passing through the quantization of the constraints, and then we focus on two Minisuperspaces of its cosmological sector. We see explicitally how the theory solves the classical singularity problem at the analytic and effective level, and replaces the physical singularity with a quantum bounce in the case of an homogeneous and isotropic model (FRW with k=0), with multiple bounces in the Bianchi I Universe (only homogeneity with commuting Killing vectors).