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. Our analysis is based on a "gauge" independent ADM-reduction of the dynamics to the physical degrees of freedom, and shows that the dynamics is isomorphic point by point in space to a billiard on a Lobachevsky plane. The Jacobi metric associated to the geodesic flow is constructed and a non-zero Lyapunov exponent is explicitly calculated. The chaos covariance emerges from the independence of the form of the lapse function and the shift vector.

arXiv comment3 pages, 1 figure, proceedings of the XI Marcel Grossmann meeting on Relativistic Astrophysics, July 23-29, 2006, Berlin