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We apply a hybrid approach which combines loop and Fock quantizations tofully quantize the linearly polarized Gowdy $T^3$ model in the presence of amassless scalar field with the same symmetries as the metric. Like in theabsence of matter content, the application of loop techniques leads to aquantum resolution of the classical cosmological singularity. Most importantly,thanks to the inclusion of matter, the homogeneous sector of the model containsflat Friedmann-Robertson-Walker (FRW) solutions, which are not allowed invacuo. Therefore, this model provides a simple setting to study at the quantumlevel interesting physical phenomena such as the effect of the anisotropies andinhomogeneities on flat FRW cosmologies.

Matter in inhomogeneous loop quantum cosmology: the Gowdy $T^3$ model