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We analyse the classical and quantum dynamics of a Bianchi I model in thepresence of a small negative cosmological constant characterizing its evolutionin term of the dust-time dualism. We demonstrate that in a canonical metricapproach, the cosmological singularity is removed in correspondence to apositive defined value of the dust energy density. Furthermore, the quantumBig-Bounce is connected to the Universe turning point via a well-definedsemiclassical limit. Then we can reliably infer that the proposed scenario iscompatible with a cyclical Universe picture. We also show how, when thecontribution of the dust energy density is sufficiently high, the proposedscenario can be extended to the Bianchi IX cosmology and therefore how it canbe regarded as a paradigm for the generic cosmological model. Finally, weinvestigate the origin of the observed cut-off on the cosmological dynamics,demonstrating how the Big-Bounce evolution can be mimicked by the samesemiclassical scenario, where the negative cosmological constant is replacedvia a polymer discretization of the Universe volume. A direct proportionalitylaw between such two parameters is then established.

Big-bounce cosmology from quantum gravity: The case of a cyclical Bianchi I universe