  The linearly polarized Gowdy $T^3$ model with a massless scalar field with
the same symmetries as the metric is quantized by applying a hybrid approach.
The homogeneous geometry degrees of freedom are loop quantized, fact which
leads to the resolution of the cosmological singularity, while a Fock
quantization is employed for both matter and gravitational inhomogeneities.
Owing to the inclusion of the massless scalar field this system allows us to
modelize flat Friedmann-Robertson-Walker cosmologies filled with
inhomogeneities propagating in one direction. It provides a perfect scenario to
study the quantum back-reaction between the inhomogeneities and the polymeric
homogeneous and isotropic background.
