COT3 - Inhomogeneous Cosmology |
Speaker_ |
Benini, Riccardo |
Co-autors |
Giovanni Montani |
Talk _ |
Covariant Description of the Inhomogeneous Mixmaster Chaos |
Abstract _ |
We outline the covariant nature of the chaos characterizing the generic cosmological solution near the initial singularity, i.e. the so-called inhomogeneous Mixmaster model. Our analysis is based on a "gauge" independent ADM-reduction of the dynamics to the physical degrees of freedom. The out-coming picture shows how the inhomogeneous Mixmaster model is isomorphic point by point in space to a billiard on a Lobachevsky plane. The existence of an asymptotic (energy-like) constant of the motion allows us to construct the Jacobi metric associated to the geodesic flow and to calculate a non-zero Lyapunov exponent in each space point. The chaos covariance emerges from the independence of our scheme of the form of the lapse function and the shift vector; the origin of this result relies on the dynamical decoupling of space points, which takes place near the singularity, due to the asymptotic approach of the potential term to infinite walls. |