Yves De Rop

Chaos in non-diagonal spatially homogeneous cosmological models in spacetime dimensions <=10

Abstract It is shown that the chaotic oscillatory behaviour, absent in diagonal homogeneous cosmological models in spacetime dimensions between 5 and 10, can be reestablished when off-diagonal terms are included.

Are Kaluza-Klein models of the universe chaotic?

The generic behavior of vacuum inhomogeneous and spatially homogeneous Kaluza-Klein models is studied in the vicinity of the cosmological singularity. It is shown that, in space-time dimensions ≥ 11, the generalized Kasner solution, with monotonic power-law behavior of the spatial distances, becomes a general solution of the Einstein vacuum field equations and that, moreover, the chaotic oscillatory behavior disappears.On the other hand, the chaotic oscillatory behavior, absent in diagonal spatially homogeneous cosmological models in space-time dimensions between 5 and 10, can be reestablished when off-diagonal terms are included.

Qualitative approach of the general vacuum Bianchi VI and VII cosmological models near the singularity

We first show that the chaos-generating terms are absent from the vacuum field equations in the case of the general Bianchi VI and VII cosmological models. According to recent studies, this proves that the Kasnerian metric is a general solution for these models in the neighborhood of the initial singularity. Then, using a method developed by Jantzen, we reduce the field equations to a nonautonomous system of order two. A numerical integration leads to the explicit four-parameter asymptotic form of a general solution, which is indeed Kasnerian in the canonical invariant basis.

Algebraic Programming in General Relativity and Cosmology

Some algebraic programs, developed recently in the framework of a collaboration between two teams of physicists from Liege and Namur, are briefly described.