  The dynamics of an inhomogeneous universe is studied with the methods of Loop
Quantum Cosmology as an example of the quantization of vacuum cosmological
spacetimes containing gravitational waves (Gowdy spacetimes). The analysis
performed at the effective level shows that: (i) The initial Big Bang
singularity is replaced (as in the case of homogeneous cosmological models) by
a Big Bounce, joining deterministically two large universes, (ii) the universe
size at the bounce is at least of the same order of magnitude as that of the
background homogeneous universe, (iii) for each gravitational wave mode, the
difference in amplitude at very early and very late times has a vanishing
statistical average when the bounce dynamics is strongly dominated by the
inhomogeneities, whereas this average is positive when the dynamics is in a
near-vacuum regime, so that statistically the inhomogeneities are amplified.
