scholarly journals Integrability of the mixmaster model

2019 ◽  
Vol 99 (2) ◽  
Author(s):  
N. Dimakis ◽  
Petros A. Terzis ◽  
T. Christodoulakis
Keyword(s):  
Mixmaster Model

scholarly journals Quantum Mixmaster as a Model of the Primordial Universe

Universe ◽  
2019 ◽  
Vol 6 (1) ◽  
pp. 7 ◽  
Author(s):  
Hervé Bergeron ◽  
Ewa Czuchry ◽  
Jean Pierre Gazeau ◽  
Przemysław Małkiewicz
Keyword(s):  
Early Universe ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Molecular Physics ◽  
Local Structures ◽  
Cosmological Scenario ◽  
Quantum Version ◽  
Formation And Evolution ◽  
Physical Features ◽  
Mixmaster Model

The Mixmaster solution to Einstein field equations was examined by C. Misner in an effort to better understand the dynamics of the early universe. We highlight the importance of the quantum version of this model for the early universe. This quantum version and its semi-classical portraits are yielded through affine and standard coherent state quantizations and more generally affine and Weyl–Heisenberg covariant integral quantizations. The adiabatic and vibronic approximations widely used in molecular physics can be employed to qualitatively study the dynamics of the model on both quantum and semi-classical levels. Moreover, the semi-classical approach with the exact anisotropy potential can be effective in the numerical integration of some solutions. Some promising physical features such as the singularity resolution, smooth bouncing, the excitation of anisotropic oscillations and a substantial amount of post-bounce inflation as the backreaction to the latter are pointed out. Finally, a realistic cosmological scenario based on the quantum mixmaster model, which includes the formation and evolution of local structures is outlined.

scholarly journals COVARIANT FEATURE OF THE MIXMASTER MODEL INVARIANT MEASURE

2002 ◽  
Vol 11 (08) ◽  
pp. 1321-1330 ◽  
Author(s):  
GIOVANNI IMPONENTE ◽  
GIOVANNI MONTANI
Keyword(s):  
Invariant Measure ◽  
Arbitrary Function ◽  
Chaotic Behavior ◽  
Time Variable ◽  
Cosmological Singularity ◽  
Constant Of Motion ◽  
Set Up ◽  
Lapse Function ◽  
Mixmaster Model ◽  
Hamiltonian Analysis

We provide a Hamiltonian analysis of the Mixmaster Universe dynamics showing the covariant nature of its chaotic behavior with respect to any choice of time variable. Asymptotically to the cosmological singularity, we construct the appropriate invariant measure for the system (which relies on the appearance of an "energy-like" constant of motion) in such a way that its existence is independent of fixing the time gauge, i.e. the corresponding lapse function. The key point in our analysis consists of introducing generic Misner–Chitré-like variables containing an arbitrary function, whose specification allows us to set up the same statistical scheme in any time gauge.

Quasi-classical and Quantum properties of the Mixmaster model

2008 ◽  
Author(s):  
Riccardo Benini ◽  
Giovanni Montani ◽  
Carlo Luciano Bianco ◽  
She-Sheng Xue
Keyword(s):  
Quantum Properties ◽  
Mixmaster Model

Mixmaster model associated to a Borcherds algebra

2017 ◽  
Vol 23 (1) ◽  
pp. 20-27 ◽  
Author(s):  
A. E. Pavlov
Keyword(s):  
Mixmaster Model

scholarly journals Chaos in Relativity and Cosmology

1999 ◽  
Vol 172 ◽  
pp. 1-16
Author(s):  
G. Contopoulos ◽  
N. Voglis ◽  
C. Efthymiopoulos
Keyword(s):  
Black Holes ◽  
General Solution ◽  
Periodic Orbits ◽  
Rest Mass ◽  
Scattering Problem ◽  
Period Doubling ◽  
Characteristic Number ◽  
Type I ◽  
Chaotic Scattering ◽  
Mixmaster Model

AbstractChaos appears in various problems of Relativity and Cosmology. Here we discuss (a) the Mixmaster Universe model, and (b) the motions around two fixed black holes, (a) The Mixmaster equations have a general solution (i.e. a solution depending on 6 arbitrary constants) of Painlevé type, but there is a second general solution which is not Painlevé. Thus the system does not pass the Painlevé test, and cannot be integrable. The Mixmaster model is not ergodic and does not have any periodic orbits. This is due to the fact that the sum of the three variables of the system (α + β + γ) has only one maximum for τ = τm and decreases continuously for larger and for smaller τ. The various Kasner periods increase exponentially for large τ. Thus the Lyapunov Characteristic Number (LCN) is zero. The “finite time LCN” is positive for finite τ and tends to zero when τ → ∞. Chaos is introduced mainly near the maximum of (α + β + γ). No appreciable chaos is introduced at the successive Kasner periods, or eras. We conclude that in the Belinskii-Khalatnikov time, τ, the Mixmaster model has the basic characteristics of a chaotic scattering problem, (b) In the case of two fixed black holes M1 and M2 the orbits of photons are separated into three types: orbits falling into M1 (type I), or M2 (type II), or escaping to infinity (type III). Chaos appears because between any two orbits of different types there are orbits of the third type. This is a typical chaotic scattering problem. The various types of orbits are separated by orbits asymptotic to 3 simple unstable orbits. In the case of particles of nonzero rest mass we have intervals where some periodic orbits are stable. Near such orbits we have order. The transition from order to chaos is made through an infinite sequence of period doubling bifurcations. The bifurcation ratio is the same as in classical conservative systems.

scholarly journals Semiclassical and quantum behavior of the mixmaster model in the polymer approach

2013 ◽  
Vol 88 (10) ◽  
Author(s):  
Orchidea Maria Lecian ◽  
Giovanni Montani ◽  
Riccardo Moriconi
Keyword(s):  
Quantum Behavior ◽  
Mixmaster Model

MIXMASTER DYNAMICS IN THE WHEELER-DEWITT FRAMEWORK

2008 ◽  
Vol 23 (08) ◽  
pp. 1244-1247
Author(s):  
RICCARDO BENINI ◽  
GIOVANNI MONTANI
Keyword(s):  
Quantum Dynamics ◽  
Classical Analysis ◽  
Full Characterization ◽  
Operator Ordering ◽  
Classical Evolution ◽  
Mixmaster Model

In this work we present an analysis of the Mixmaster model in the Wheeler-DeWitt framework. After a brief review of the classical evolution, several aspects of the semi-classical and of the quantum dynamics are discussed: the most important results we will present are a possible operator ordering obtained from the semi-classical analysis and the full characterization of the quantum dynamics in Misner-Chitré like variables.

Ergodic theory of the mixmaster model in higher space-time dimensions

1987 ◽  
Vol 290 ◽  
pp. 111-136 ◽  
Author(s):  
Yves Elskens ◽  
Marc Henneaux
Keyword(s):  
Ergodic Theory ◽  
Space Time ◽  
Mixmaster Model

scholarly journals Chaos removal inR+qR2gravity: The mixmaster model

2014 ◽  
Vol 90 (10) ◽  
Author(s):  
Riccardo Moriconi ◽  
Giovanni Montani ◽  
Salvatore Capozziello
Keyword(s):  
Mixmaster Model
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