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A quantum analysis of the vacuum Bianchi IX model is performed, focusing inparticular on the chaotic nature of the system. The framework constructed hereis general enough for the results to apply in the context of any theory ofquantum gravity, since it includes only minimal approximations that make itpossible to encode the information of all quantum degrees of freedom in thefluctuations of the usual anisotropy parameters. These fluctuations aredescribed as canonical variables that extend the classical phase space. In thisway, standard methods for dynamical systems can be applied to study the chaosof the model. Two specific methods are applied that are suitable fortime-reparameterization invariant systems. First, a generalized version of theMisner-Chitre variables is constructed, which provides an isomorphism betweenthe quantum Bianchi IX dynamics and the geodesic flow on a suitable Riemannianmanifold, extending, in this way, the usual billiard picture. Secondly, thefractal dimension of the boundary between points with different outcomes in thespace of initial data is numerically analyzed. While the quantum system remainschaotic, the main conclusion is that its strength is considerably diminished byquantum effects as compared to its classical counterpart.

The chaotic behavior of the Bianchi IX model under the influence of quantum effects