MG14 - Talk detail

Back to previous page

 Participant

Institution

Session

Accepted

Order

Time

Talk

Title

Abstract

We examine the dynamics of a Bianchi IX model with three scale factors on a 4-dim Lorentzian brane embedded in a 5-dim de Sitter bulk with a timelike extra dimension. Einstein’s equations on the brane reduces to a 6-dim Hamiltonian dynamical system with additional terms that implement nonsingular bounces in the early phase of the universe. The phase space presents two critical points (a saddle-center-center and a center-center-center) in a finite region of phase space, and two asymptotic de Sitter critical points at infinity. The critical points belong to a 2-dim invariant plane and together organize the dynamics of the phase space. The saddle-center-center engenders in phase space the topology of stable and unstable 4-dim cylinders R × S^3 , where R is a saddle direction and S^3 is the center manifold of unstable periodic orbits, the latter being the nonlinear extension of the center-center sector. By a proper canonical transformation we are able to separate the three degrees of freedom of the dynamics into one degree connected with the expansion and/or contraction of the scales of the model, and two pure rotational degrees of freedom associated with the center manifold S^3. The typical dynamical flow is an oscillatory mode about the orbits of the invariant plane. For the stable and unstable cylinders we have the oscillatory motion about the separatrix towards the bounce, leading to the homoclinic transversal intersection of the cylinders, as shown numerically in two distinct experiments. We show that the homoclinic intersection manifold has the topology of R × S^2 consisting of homoclinic orbits biasymptotic to the center manifold S^3. This behavior defines a chaotic saddle associated with S^3, indicating that the intersection manifold has the nature of a Cantor set with a compact support S^2, being an invariant signature of chaos in the model. We discuss possible connections with analogous features in the BKL conjecture in general relativity.

Pdf file

Back to previous page