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Abstract

We perform the quantization of an inhomogeneous cosmological spacetime that contains a matter scalar field within the framework of the Loop Quantum Cosmology. More specifically, we quantize the linearly polarized Gowdy cosmologies with three-torus topology in the presence of a massless scalar field. After a gauge fixing procedure, only two global constraints remain in the system. The degrees of freedom associated with the subfamily of homogeneous solutions, which describe Bianchi I cosmologies, are quantized by using a polymeric quantization. A Fock quantization is used for the inhomogeneous degrees of freedom of both the gravitational waves and the matter scalar field. This hybrid quantization assumes a hierarchy in the relevance of the loop quantum phenomena, so that the more important effects are due to the homogeneous modes. The initial cosmological singularity that appears in the classical solutions is resolved at the kinematical level. In addition, a standard quantum description of the inhomogeneities is recovered. The inclusion of matter in the Gowdy model lead to more physically interesting model that allows us to study, in some regimes, the effect of the anisotropies and inhomogeneities on flat Friedmann-Robertson-Walker cosmologies.