  The quantum dynamics of the linearly polarized Gowdy T^3 model (compact
inhomogeneous universes admitting linearly polarized gravitational waves) is
analyzed within Loop Quantum Cosmology by means of an effective dynamics. The
analysis, performed via analytical and numerical methods, proves that the
behavior found in the evolution of vacuum (homogeneous) Bianchi I universes is
preserved qualitatively also in the presence of inhomogeneities. More
precisely, the initial singularity is replaced by a big bounce which joins
deterministically two large classical universes. In addition, we show that the
size of the universe at the bounce is at least of the same order of magnitude
(roughly speaking) as the size of the corresponding homogeneous universe
obtained in the absence of gravitational waves. In particular, a precise lower
bound for the ratio of these two sizes is found. Finally, the comparison of the
amplitudes of the gravitational wave modes in the distant future and past shows
that, statistically (i.e., for large samples of universes), the difference in
amplitude is enhanced for nearly homogeneous universes, whereas this difference
vanishes in inhomogeneity dominated cases. The presented analysis constitutes
the first systematic effective study of an inhomogeneous system within Loop
Quantum Cosmology, and it proves the robustness of the results obtained for
homogeneous cosmologies in this context.
