The Mixmaster Universe: the final reckoning?

  title={The Mixmaster Universe: the final reckoning?},
  author={Konstantinos Andriopoulos and P. G. L. Leach},
  journal={Journal of Physics A: Mathematical and Theoretical},
The investigation of the Mixmaster Universe using singularity analysis has attracted much attention in recent years and produced a variety of interpretations, some of which have been supported by numerical experimentation. We present a new singularity analysis and make direct comparisons with systems of known dynamical behaviour to avoid making unwarranted inferences and remove the controversy surrounding the Mixmaster Universe. 

The occurrence of a triple -1 resonance in the standard singularity analysis

Any careful singularity analysis of the Mixmaster Universe uncovers the instance of a triple -1 resonance. The Mixmaster Universe does not exhibit a closed-form solution and so a correct

BKL Method in the Bianchi IX Universe Model Revisited

Given the extreme difficulty in finding analytical solutions to Einstein’s equations for universe models, such as the Bianchi type IX, different physical-mathematical techniques have been designed to

Free Motion around Black Holes with Disks or Rings: Between Integrability and Chaos–V

The complete integrability of geodesic motion, the well-known feature of fields of isolated stationary black holes, can easily be “spoiled” by the presence of some additional sources (even if highly

Integrability of the mixmaster model

We make use of a generalized definition of a class of nonlocal conserved charges in phase space to demonstrate that the anisotropic Bianchi type IX model in vacuum is (at least locally) Liouville

New insights into singularity analysis

Abstract In this work, we emphasize the use of singularity analysis in obtaining analytic solutions for equations for which standard Lie point symmetry analysis fails to make any lucid decision. We

Quantum cosmology of Bianchi VIII, IX LRS geometries

In the present work we revisit the axisymmetric Bianchi VIII and IX models. At the classical level we reproduce the known analytic solution, in a novel way making use of two quadratic integrals of

Bianchi IX cosmologies in the Einstein-Skyrme system in a sector with nontrivial topological charge

The dynamics of the most general Bianchi IX cosmology with three time dependent scale factors for the Einstein-Skyrme system is analyzed. For the Skyrmion, a generalized hedgehog ansatz with unit

Free motion around black holes with discs or rings: between integrability and chaos - II: Chaos around black holes with discs or rings

Geodesic dynamics is regular in the fields of isolated statio n ry black holes. However, due to the presence of unstable periodic orbits, it easily becomes chaotic under various perturbations. Here

Singularity and symmetry analyses of mathematical models of epidemics.

We present a summary of the methods of Lie symmetry and Painleve singularity analyses and apply them to a number of wellknown epidemiological models to demonstrate the utility of these analyses in

Some properties of the Nesterenko differential sequence

Abstract We present some properties of a differential sequence prompted by a formula in a paper by Maryna Nesterenko (International Journal of Mathematics and Mathematical Sciences 2006 (2006),



The mixmaster universe model, revisited

We re-examine the singularity structure of the mixmaster universe model based on recent developments concerning the treatment of negative resonances. In a previous publication we have shown that this

Painleve analysis for the mixmaster universe model

We show that the mixmaster universe, or Bianchi IX, model passes the Painleve test in the form of the Ablowitz-Ramani-Segur algorithm, i.e. the solutions of the equations of motion do not have

The last remake of the mixmaster universe model

We review the existing evidence on the (non)integrability of the mixmaster universe model. We show how a local Painleve analysis can be used to study the possible existence of essential

The Mixmaster universe: A Chaotic Farey tale

When gravitational fields are at their strongest, the evolution of spacetime is thought to be highly erratic. Over the past decade debate has raged over whether this evolution can be classified as

Painleve analysis of the mixmaster universe

We analyse the behaviour of the mixmaster universe in the context of general relativity by applying methods from the geometric theory of dynamical systems in the complex plane and in particular by

Analysis of an FRW cosmological model

The Einstein field equations for the Friedmann universe reduce to a system of three first-order equations for the space-like components and a constraint from the temporal component. We analyse the

Non-integrability of the mixmaster universe

We comment on an analysis by Contopoulos et al.(1993) which demonstrates that the governing six-dimensional Einstein equations for the mixmaster spacetime metric pass the ARS or reduced Painleve

On the exact solutions of the Bianchi IX cosmological model in the proper time

It has recently been argued that there might exist a four-parameter analytic solution to the Bianchi IX cosmological model, which would extend the three–parameter solution of Belinskii et al. to one

Evidence of a natural boundary and nonintegrability of the mixmaster universe model

SummaryThe formal asymptotic analysis of Latifi et al. [4] suggests that the Mixmaster Universe model possesses movable transcendental singularities and thus is nonintegrable in the sense that it