Cosmolog\'ia Cu\'antica de Lazos: Anisotrop\'ias e Inhomogeneidades
  Loop Quantum Cosmology adapts the techniques of Loop Quantum Gravity in the quantization of homogeneous cosmological models obtained from General Relativity by symmetry reduction. As a necessary step towards the extraction of realistic results from Loop Quantum Cosmology, we should consider the inclusion of inhomogeneities, which play a central role in current cosmology. The main goal of this thesis is to progress in this direction. With this aim we have studied a natural test bed to incorporate inhomogeneities in Loop Quantum Cosmology: the linearly polarized Gowdy T3 model. This model can be regarded as a homogeneous Bianchi I background filled with inhomogeneities propagating in one direction. We have completed its quantization by means of a hybrid approach, that combines the loop quantization of the homogeneous sector, within the so-called improved dynamics scheme, with a Fock quantization for the inhomogeneities. In order to perform this quantization as thorough as possible, we have also reviewed the (improved dynamics) loop quantization of flat FRW cosmologies, paradigmatic model in LQC, as well as that of the Bianchi I model. We have proposed a new prescription for the Hamiltonian constraint operator of these models, that displays nicer features than those of previous proposals. In particular, we get simpler superselection sectors with a global and well-understood Wheeler-DeWitt limit in the large volume regime, which serve to improve our understanding of the physical Hilbert space of these models. 
Mercedes Mart\'in-Benito
gr-qc