Classical and quantum aspects of Bianchi type IX cosmological model

A detailed study of the Bianchi type IX cosmological model is done. Classical field equations are discussed with a massive scalar field. The Wheeler-DeWitt quantum equation is formed and is solved using a Born-Oppenheimer type of approximation.     

Comparing the dynamics of diagonal and general Bianchi IX spacetime

The European Physical Journal C - Loop quantum gravity (LQG) is a theory that proposes a way to model the behavior of the spacetime in situations where its atomic characteristic arises. Among these...     

Bianchi type IX string cosmological model in general relativity

We have investigated Bianchi type IX string cosmological models in general relativity. To get a determinate solution, we have assumed a condition ρ=λ i.e. rest energy density for a cloud of strings is equal to the string tension density. The various physical and geometrical aspects of the models are also discussed.     

Gravitational fields with space-times of Bianchi type IX

Spatially homogeneous space-times of Bianchi type IX are considered. A general scheme for the derivation of exact solutions of Einstein’s equations corresponding to perfect fluid plus pure radiation fields is outlined. Some simple rotating Bianchi type IX cosmological models are presented. The details of these solutions are also discussed. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Compact invariant sets of the Bianchi VIII and Bianchi IX Hamiltonian systems

In this Letter we prove that all compact invariant sets of the Bianchi VIII Hamiltonian system are contained in the set described by several simple linear equalities and inequalities. Moreover, we describe invariant domains in which the phase flow of this system has no recurrence property and show that there are no periodic orbits and neither homoclinic, nor heteroclinic orbits contained in the zero level set of its Hamiltonian. Similar results are obtained for the Bianchi IX Hamiltonian system.     

Relativistic dynamics of spherical timelike shells

The dynamics of general relativistic timelike spherically symmetric thin shells of matter is considered, putting special emphasis on the physical interpretation of the models and, therefore, on the dependence of the dynamical behavior upon then the choice of the equation of state. From this point of view the general formalism is reviewed both in the Israel’s and in the canonical (Lagrangian and Hamiltonian) approach. Known exact solutions corresponding to closed equations of state are reviewed as well, and a new, wide class of nonlinear barotropic solutions is introduced and discussed in detail.     

Quantum fluctuations and nonavoidance of the singularity in Bianchi type I cosmology

An effective metric is defined and used for analyzing the quantum fluctuations in a classical geometry. Earlier work showing that quantum (conformal) fluctuations avoid the classical singularity in the case of spherically symmetric collapse is briefly reviewed. It is shown that this result doesnot extend to anisotropic Bianchi type I cosmology. Here the dispersion in the fluctuations increases too slowly to quench the classical singularity. The singularity persists in the space-time described by the effective metric.     

Quantum Origin of a Rotating Universe of the Bianchi IX Type

A closed cosmological model with rotation of the Bianchi IX type is constructed. Λ-term and anisotropic liquid are the sources of gravitational field for the model. A quantum origin of the Universe is examined. The Wheeler — De Witt equation is derived. A tunneling coefficient for the Universe is calculated. It is found for a particular case that the probability of quantum birth of a rotating Universe is higher than for the model without rotation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 71–75, June, 2005.     

Classical and Quantum Evolution of the Bianchi Type I Model

The classical and quantum evolution of an anisotropic cosmological Bianchi type I model is considered. In the classical case, the influence of the minimally coupled scalar field is taken into account. Thus the system of two equations is obtained, which are explored at the inflationary and scalaron stages. The quantum problem in view of the positive cosmological constant is considered. The principal moment of the account of an anisotropy is the occurrence of the potential barrier unbounded in zero and at infinity. Though the greatest value of the potential is less than zero and the total energy of the Universe E=0, there is an important opportunity for above-barrier reflection of the wave function of the Universe. After reflection the wave function describes the expanding Universe promptly losing anisotropy and transferring into the Friedmann Universe.     

Anisotropic Bianchi VIII/IX cosmological models with matter and electromagnetic fields

We present a class of cosmological solutions of Einstein equations, with matter and electromagnetic field, which are anisotropic and spatially homogeneous of Bianchi types VIII and IX.     

Classical and quantum properties of a two-sphere singularity

Recently Böhmer and Lobo have shown that a metric due to Florides, which has been used as an interior Schwarzschild solution, can be extended to reveal a classical singularity that has the form of a two-sphere. Here the singularity is shown to be a naked scalar curvature singularity that is both timelike and gravitationally weak. It is also shown to be a quantum singularity because the Klein–Gordon operator associated with quantum mechanical particles approaching the singularity is not essentially self-adjoint.     

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.     

Bianchi type-II cosmological model with viscous fluid

A spatially homogeneous and locally rotationally symmetric Bianchi type-II cosmological model under the influence of both shear and bulk viscosity has been studied. Exact solutions are obtained with a barotropic equation of state (p=) and considering the linear relationships between, ², and ², which represent the fluid density, the expansion, and the shear scalars, respectively. Special cases with vanishing bulk viscosity coefficients and with the perfect fluid in the absence of viscosity have also been studied. The formal appearance of the solutions is the same for both the viscous as well as the perfect fluids. The difference is only in choosing a constant parameter which appears in the solutions. In the cases of either a fluid with bulk viscosity alone or a perfect fluid, the barotropic equation of state is no longer an additional assumption to be imposed; rather it follows directly from the field equations.