Jacques Demaret

Non-oscillatory behaviour in vacuum Kaluza-Klein cosmologies

Abstract It is argued that the generalized Kasner solution, with monotonic power-law behaviour of the spatial distances, becomes a general solution of the Einstein vacuum field equations near the cosmological singularity in spacetime dimensions ⩾11.

The fate of the mixmaster behaviour in vacuum inhomogeneous Kaluza-Klein cosmological models☆

Abstract The generic behaviour of vacuum inhomogeneous Kaluza-Klein cosmologies is studied in the vicinity of the cosmological singularity. The collision law for the Kasner exponents is calculated in any number of spatial dimensions d . Its properties are investigated both theoretically and numerically. It is argued that the chaotic oscillatory behaviour disappears for d ⩾ 10. This regime is replaced by the monotonic Kasner behaviour found previously.

Cosmological models in eleven-dimensional supergravity

Abstract Spatially homogeneous, anisotropic, cosmological models are investigated in the case of D = 11 supergravity. It is shown how the field equations reduce with this assumption to ordinary differential equations with respect to time. These equations are solved when the homogeneity group is abelian and admits non-trivial solutions with various splittings of the 11 dimensions into n + (11 − n). Other exact solutions with different homogeneity groups are exhibited, one of them being such that the physical dimensions expand much faster than the extra ones.

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.

Exact solution for vacuum Bianchi type III model with a cosmological constant

An exact analytic particular solution for a vacuum Bianchi type III model with a cosmological constant Lambda is derived: its properties are briefly discussed. In particular, the solution for Lambda <0 describes an anisotropic spatially homogeneous model evolving from a pancake singularity towards a barrel singularity.

The fractal nature of the power spectrum as an indicator of chaos in the Bianchi IX cosmological model

Abstract Using two different methods, we compute the fractal dimension of the power spectrum associated with numerical solutions of the spatially homogeneous Bianchi IX cosmological model in Misner-Chitre coordinates. According to Perdands criterion, the noninteger character of this dimension is reflection of chaos and can be used to measure it, in the same spirit as the Lyapunov exponent of the Kolmogorov entropy. The results obtained indicate the chaotic nature of the behavior of the Bianchi IX model near the cosmological singularity.

A constant equation of state for quintessence

Quintessence is often invoked to explain the universes acceleration suggested by type Ia supernovae observations. The aim of this letter is to study the validity of using a constant equation of state for quintessence models. We shall show that this hypothesis strongly constraint the form of the scalar potential.

Painlevé singularity analysis of the perfect fluid Bianchi type-IX relativistic cosmological model

We perform the Painleve test (i.e. the Kowalevskaya - Gambier test or the perturbative test) for the perfect fluid Bianchi type-IX relativistic cosmological model, in order to predict some probable chaotic regimes. This technique enables us to detect every single-valued particular solution associated with a given relativistic dynamical system. Several physically interesting cases are studied. These include radiation-dominated and matter-dominated universes, the case of a cosmological constant and the case of the so-called stiff-matter. In all cases but the cosmological constant case, the models studied do not pass the Painleve test, exhibit infinitely many movable logarithms and are therefore probably chaotic. Moreover, we show that some physically interesting single-valued particular solutions present in the vacuum case cannot subsist for a perfect fluid cosmological model. In particular, in the radiation and dust cases, we show that there cannot exist any exact and closed-form axisymmetric solution.

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.

Hamiltonian formulation of Bianchi cosmological models in quadratic theories of gravity

We use Boulwares Hamiltonian formalism of quadratic gravity theories in order to analyse the classical behaviour of Bianchi cosmological models for a Lagrangian density in four spacetime dimensions. For this purpose we define a canonical transformation which leads to a clear distinction between two main variants of the general quadratic theory, i.e. for or conformal Lagrangian densities. In this paper we restrict the study to the first variant. For the Bianchi-type I and IX models, we give the explicit forms of the super-Hamiltonian constraint, of the ADM Hamiltonian density and of the corresponding canonical equations. In the case of a pure quadratic theory , we solve them analytically for the Bianchi I model. For the Bianchi-type IX model, we reduce the first-order equations of the Hamiltonian system to three coupled second-order equations for the true physical degrees of freedom. This discussion is extended to isotropic FLRW models.