Bianchi type-IX Cosmological Model Research Articles

Bianchi Type-IX Cosmological Model in Self-Creation Theory of Gravitation

In this paper, we study macroscopic body cosmological model in the context of self-creation theory. We solve field equations by using relation between metric coefficients and equation of state for macroscopic body. Also, we discuss the features of the obtained solutions.

Spinor field in Bianchi type-IX space–time

Within the scope of Bianchi type-IX cosmological model we have studied the role of spinor field in the evolution of the Universe. It is found that unlike the diagonal Bianchi models in this case the components of energy–momentum tensor of spinor field along the principal axis are not the same (i.e., [Formula: see text]), even in the absence of spinor field nonlinearity. The presence of nontrivial non-diagonal components of energy–momentum tensor of the spinor field imposes severe restrictions both on geometry of space–time and on the spinor field itself. As a result the space–time turns out to be either locally rotationally symmetric or isotropic. In this paper we considered the Bianchi type-IX space–time both for a trivial b, that corresponds to standard Bianchi type-IX and the one with a non-trivial b. It was found that a positive self-coupling constant λ1 gives rise to an oscillatory mode of expansion, while a trivial λ1 leads to rapid expansion at the early stage of evolution.

Spectral action for Bianchi type-IX cosmological models

A rationality result previously proved for Robertson-Walker metrics is extended to a homogeneous anisotropic cosmological model, namely the Bianchi type-IX minisuperspace. It is shown that the Seeley-de Witt coefficients appearing in the expansion of the spectral action for the Bianchi type-IX geometry are expressed in terms of polynomials with rational coefficients in the cosmic evolution factors w_1(t), w_2(t), w)3(t), and their higher derivates with respect to time. We begin with the computation of the Dirac operator of this geometry and calculate the coefficients a_0 ,a_2 ,a_4 of the spectral action by using heat kernel methods and parametric pseudodifferential calculus. An efficient method is devised for computing the Seeley-de Witt coefficients of a geometry by making use of Wodzicki’s noncommutative residue, and it is confirmed that the method checks out for the cosmological model studied in this article. The advantages of the new method are discussed, which combined with symmetries of the Bianchi type-IX metric, yield an elegant proof of the rationality result.

Bianchi Type-IX Cosmological Model with a Perfect Fluid in f(R) Theory of Gravity

Bianchi Type-IX Cosmological Model with a Perfect Fluid in f(R) Theory of Gravity

Bianchi Type-IX Anisotropic Dark Energy Cosmological Models with Time Dependent Deceleration Parameter

Bianchi type-IX cosmological models with variable equation of state (EoS) parameter have been investigated in general relativity when universe is filled with dark energy. The field equations have been solved by considering (i) q=B (variable); (ii) , where k and m are constants; (iii) , where k is constant and R is average scale factor; (iv) which gives . This renders early decelerating and late time accelerating cosmological models. The physical and geometrical properties of the models are also discussed.

Bianchi Type-IX Magnetized Dark Energy Model in Saez-Ballester Theory of Gravitation

The Bianchi type-IX cosmological model with variable ω has been studied in the scalar tensor theory of gravitation proposed by Saez and Ballester [Phys. Lett. A 113: 467, 1985] in the presence and absence of magnetic field of energy densityρb. A special law of variation of Hubble’s parameter proposed by Berman [Nuovo Cimento 74 B, 182, 1983] has been used to solve the field equations. The physical and kinematical properties of the model are also discussed.

Statefinder Diagnostic for Binary Mixture of Anisotropic Dark Energy and Perfect Fluid in Bianchi Type-IX Universe

The new Bianchi type-IX cosmological models with binary mixture of perfect fluid and anisotropic dark energy have been studied. The unique solution of field equations is obtained by assuming that the energy conservation equation of the perfect fluid and dark energy vanishes separately together with a special law for the mean Hubble parameter (Berman, 1983) which yields a constant value of the deceleration parameter and generates two types of solutions, one is of power law type and other is of the exponential type. To have a general description of an anisotropic dark energy component in terms of its equation of state

Inflation in Bianchi type-IX Einstein-Cartan cosmological model

Within the framework of Einstein-Cartan theory with Weyssenhoff fluid, we investigate an inflation model for an anisotropic Bianchi type-IX cosmological model. The system of field equations is solved numerically and an inflation epoch is achieved. The general condition for the inflation to occur is also discussed. This anisotropic model evolves quickly towards to an isotropic one.

Dynamical behavior of Lagrangian systems on Finsler manifolds

In this paper we develop a theoretical framework devoted to a geometrical description of the behavior of dynamical systems and their chaotic properties. The underground manifold is a Finsler space whose features permit the description of a wide class of dynamical systems such as those with potentials depending on the time and velocities for which the Riemannian approach is unsuitable. Another appealing feature of this more general setting relies on its very origin: Finsler spaces arise in a direct way on imposing the invariance for time reparametrization to a standard variational problem. A Finsler metric is a generalization of the well-known Jacobi and Eisenhart-metrics for conservative dynamical systems. We use this geometry to derive the main geometrical invariants and related expressions that are needed to establish the transition to chaos in very general Lagrangian systems. In order to point out the versatility and the effectiveness of this extension of the geometrical approach, we suggest the introduction of this formalism to some interesting dynamical systems for which the Finsler metric is much more suitable than the Riemannian one. In particular, we present the following: (i) an exhaustive description and numerical results for a resonant oscillator with a time-dependent potential, (ii) an exact description (without any approximation) of the dynamics of Bianchi type-IX cosmological models, and (iii) a geometrical description of the restricted three-body problem whose effective potential depends linearly on the velocities. In the first case, the numerical integration of the geodesics and geodesic deviation equations shows that in the geometrical picture the source of the exponential instability of trajectories relies on the mechanism of parametric resonance and does not originate from the negativity of curvature.

Mixmaster universe in fourth-order gravity theories.

We analyze the behavior of the Bianchi type-IX cosmological model in the full fourth-order theory of gravity in four space-time dimensions on approach to the singularity both analytically and numerically. By directly analyzing the full fourth-order field equations we prove explicitly that the Belinski-Khalatnikov-Lifshitz (BKL) analytic solution (and the accompanying bounce law) is also a solution to the more general case that we consider. But it appears to be nongeneric, because a perturbation analysis shows that power-law Kasner asymptotes are unstable on approach to the singularity. On the other hand, we find that the model possesses a stable isotropic monotonic power-law asymptotic solution and accordingly we show that there is a general solution which is nonchaotic near the space-time singularity. Numerical experiments confirm the existence of such a behavior. The inclusion of matter fields does not alter the evolution in the neighborhood of the singularity. The role of space-time dimensionality on the chaotic evolution of the mixmaster universe in these theories is also spelled out. In particular, we show that it is impossible to build a mixmaster universe in space-time dimensions higher than four in the full fourth-order gravity theory based on the BKL approximation scheme.

Anisotropic diagonal Bianchi type-IX minisuperspace with N=4 supersymmetry.

Spatially homogeneous anisotropic diagonal Bianchi type-IX cosmological models are extended to N=4 supersymmetry arising naturally from N=1 supergravity by dimensional reduction. The solutions of the quantized angular momentum and supersymmetry constraints in the empty and filled fermion sectors are given, and it is shown that these solutions are the only ones proving a very recent conjecture by D'Eath, Hawking, and Obreg\'on.

Invariant Lyapunov exponents and chaos in cosmology.

The precise dynamical nature of the Bianchi type-IX cosmological model has been a subject of debate for a number of years. The lack of congruence between various results, which mainly employ numerical calculations of the spectrum of Lyapunov exponents, has motivated a number of attempts at a gauge-invariant characterization of chaos. Here we critically examine one of these attempts and argue that none of the attempted characterizations so far put forward are completely satisfactory. We also briefly discuss natural gauges in cosmology and distinguish between qualitative and quantitative measures of chaos.

Dynamics of multidimensional generalization of Bianchi type-IX cosmological models.

We investigate the dynamics of an 11-dimensional homogeneous cosmological model. We assume that the t=const hypersurfaces are products of a 3-dimensional Bianchi type-IX space and a 7-dimensional torus. Most results of our investigation hold when the 7-dimensional torus is replaced by an m-dimensional torus ${T}^{m}$. We show that for a large class of vacuum solutions the physical space expands while the microspace contracts providing a natural mechanism of dimensional reduction. Matter satisfying a simple barotropic equation of state always breaks the process of dynamical dimensional reduction. With special attention we study the behavior of our model close to the initial singularity. In contrast with the 4-dimensional Bianchi type-IX cosmological model the Kasner solution always describes an approach to the initial singularity. We study the transition from the Kasner regime to the oscillatory regime. We show that matter does not significantly change this property. We have found some exact solutions; they describe isotropic physical space, and axially symmetric physical space. We also investigate high-temperature quantum effects and their effects on the dynamics of our model. We show that the high-temperature quantum corrections do not depend on the geometrical properties of space, provided it is compact. The high-temperature quantum corrections can be described by a macroscopic equation of state satisfied by radiation.

Transition of rotating Bianchi type-IX cosmological model into an inflationary era.

A Bianchi type-IX cosmological model has been found as a solution of Einstien's vacuum field equations with a cosmological constant. The solution represents a rotating generalziation fo the de Sitter universe. This universe shows a transition to exponential expansion and the vorticity begins to decay exponentially at the grand-unified-theory time. The point of time for this transition is independent of the magnitude of the vorticity. During the Guth inflationary era the vorticity decays by a factor of the order ${10}^{\mathrm{\ensuremath{-}}142}$.

Fluctuations produced by the cosmological constant in the empty Bianchi type-IX model

We analyze the fluctuations of the gravitational field, produced by the cosmological term, in the empty Bianchi type-IX cosmological model. It is shown that such fluctuations do not change the process of alternation of Kasner eras very near to the singularity, and that a positive cosmological constant leads to an asymptotic isotropization of the model.