  For the Bianchi type I space-time (vacuum or with a massless scalar field),
the loop quantum cosmology bounce can be viewed as a rapid transition between
two classical solutions, with a simple transformation rule relating the Kasner
exponents of the two epochs. This transformation rule can be extended to other
Bianchi space-times under the assumption that during the loop quantum cosmology
bounce the contribution of the spatial curvature to the Hamiltonian constraint
is negligible compared to the kinetic terms. For the vacuum Bianchi type IX
space-time there are transformation rules for how each of the parameters
characterizing the Kasner epochs change during the bounce. This provides a
quantum gravity extension to the Mixmaster dynamics of general relativity, and
may have interesting implications for the Belinski-Khalatnikov-Lifshitz
conjecture.
