Sara Fernandez Uria (University of the Basque Country, Spain)

Bianchi IX dynamics under the influence of quantum-geometry effects

According to the Belinski-Khalatnikov-Lifshitz conjecture, the Bianchi IX model describes the evolution of each spatial point close to a generic spacelike singularity. However, near the singularity, quantum effects are expected to be relevant, and, consequently, in this work, a quantum analysis of the model is performed by considering quantum-geometry effects. In particular, we perform two different semiclassical approximations, each tailored for a specific study: obtain the modifications of the transition laws and study the chaotic nature. The latter will be the main focus of the talk, as it provides the most interesting results. Specifically, with the mentioned approximation, we are able to encode all the information of the quantum degrees of freedom in certain canonical variables, thus expanding the classical phase space. In this way, we can apply the usual methods of dynamical systems for studying chaos. In particular, two techniques are considered. On the one hand, an analytical study is carried out, which provides an isomorphism between the quantum dynamics of Bianchi IX and a geodesic flow on a Riemannian manifold. On the other hand, by means of numerical simulations, the fractal dimension of the boundary between points with different outcomes in the space of initial conditions is computed. The main conclusion is that, although the quantum system is chaotic, the quantum effects considerably reduce this behavior compared to its classical counterpart.