Big Bounce and inhomogeneities

Abstract

The dynamics of an inhomogeneous universe is studied with the methods of loop quantum cosmology, via a so-called hybrid quantization, as an example of the quantization of vacuum cosmological spacetimes containing gravitational waves (Gowdy spacetimes). The analysis of this model with an infinite number of degrees of freedom, 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 and (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.