Related papers: Symbolic Dynamics, Modular Curves, and Bianchi IX …
All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them…
We analyze the Bianchi IX Universe in the Polymer Quantum Mechanics framework by facing both semiclassical and purely quantum effects near the cosmological singularity. We adopt Misner variables to describe the model dynamics, applying the…
We investigate Bianchi type IX ''Mixmaster'' universes within the framework of the low-energy tree-level effective action for string theory, which (when the ''stringy'' 2-form axion potential vanishes) is formally the same as the…
This paper begins with a short presentation of the Bianchi IX or ``Mixmaster'' cosmological model, and some ways of writing the Einstein equations for it. There is then an interlude describing how I came to a study of this model, and then a…
We examine the dynamics of a Bianchi IX model on a 4-dim brane embedded in a 5-dim conformally flat empty bulk with a timelike extra dimension. Einstein's equations on the brane reduces to a 6-dim Hamiltonian dynamical system with…
We consider an evolution of anisotropic cosmological model on the example of the Bianchi type I homogeneous universe. It is filled by the mixture of matter and dark energy with an arbitrary barotropic equation of state (EoS). The general…
An approach to quantum cosmology, relying on strengths of both canonical and path integral formalisms, is applied to the cosmological model, Bianchi type IX. Physical quantum states are constructed on the maximal slice of the cosmological…
We develop a relativistic framework to investigate the evolution of cosmological structures from the initial density perturbations to the highly nonlinear regime. Our approach involves proposing a procedure to match ``best-fit", exact…
In this work we explore the quantum Bianchi type IX-model, its semi-classical features, and its relevance in early cosmology to tentatively explain inflation and production of primordial structures. We specially focus on the analytical and…
A quantum analysis of the vacuum Bianchi IX model is performed, focusing in particular on the chaotic nature of the system. The framework constructed here is general enough for the results to apply in the context of any theory of quantum…
The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for…
Spatially homogeneous cosmological models reduce to Hamiltonian systems in a low dimensional Minkowskian space moving on the total energy shell $H=0$. Close to the initial singularity some models (those of Bianchi type VIII and IX) can be…
Recently we have studied the Lorentzian version of the IIB matrix model as a nonperturbative formulation of superstring theory. By Monte Carlo simulation, we have shown that the notion of time ---as well as space---emerges dynamically from…
We find instanton/cosmological solutions with biaxial Bianchi-IX symmetry, involving non-trivial spatial dependence of the $\bbbc P^{1}$- and $\bbbc P^{2}$-sigma-models coupled to gravity. Such manifolds arise in N=1, $d=4$ supergravity…
We study the dynamics of anisotropic Bianchi type-IX models with matter and cosmological constant. The models can be thought as describing the role of anisotropy in the early stages of inflation. The concurrence of the cosmological constant…
We investigate a model of gravitational collapse of matter inhomogeneities where the latter are modelled as Bianchi type IX (BIX) spacetimes. We found that this model contains, as limiting cases, both the standard spherical collapse model…
We analyse the classical and quantum dynamics of a Bianchi I model in the presence of a small negative cosmological constant characterizing its evolution in term of the dust-time dualism. We demonstrate that in a canonical metric approach,…
We study the dynamics of the vacuum Bianchi IX model with timelike singularity and compare it with the dynamics of the Bianchi IX model with cosmological singularity. We show that differences in the signs of some terms in the set of…
Numerical investigation of a class of inhomogeneous cosmological spacetimes shows evidence that at a generic point in space the evolution toward the initial singularity is asymptotically that of a spatially homogeneous spacetime with…
Previous studies \cite{berger98a} have provided strong support for a local, oscillatory approach to the singularity in U(1) symmetric, spatially inhomogeneous vacuum cosmologies on $T^3 \times R$. The description of a vacuum Bianchi type…