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Hybrid quantization of the Gowdy model within loop quantum cosmology

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Loop quantum
cosmology (LQC) proposes a quantization for homogeneous cosmologies which
success in solving the classical singularity problem. Realistic scenarios call
for the consideration of inhomogeneities. Focusing on the simplest inhomogenous
cosmological model, the Gowdy model with three-torus spatial topology
and linearly polarized gravitational waves, I'll describe an approach to treat
inhomogeneities in the framework of loop quantum cosmology. This is a hybrid
approach that combines LQC methods with Fock quantization. Furthermore, I'll
discuss justified approximations that allow us to find approximate solutions to
the (very complicated) Hamiltonian constraint of the model.