Anisotropic Cosmological Models Research Articles

Bianchi Type-V Cosmological Models for Perfect Fluid with Time-Varying Gravitational and Cosmological Constant

Einstein’s field equations with variable gravitational and cosmological constants are considered in presence of perfect fluid for locally-rotationally-symmetric (LRS) Bianchi type-V space-time discussion in context of the particle creation. We present new shear free solutions for both absence and presence of particle creation. The solution describes the particle and entropy generation in the anisotropic cosmological models. We observe that time variation of gravitational and cosmological constant is needed for particle creation phenomena. Moreover, we obtained the particle production rate Γ(t) for this model and discussed in detail.

Thermodynamics and small temporal variations in the equations of state of anisotropic cosmological models of Petrov type D

Thermodynamics and small temporal variations in the equations of state of anisotropic cosmological models of Petrov type D

Unitary evolution for anisotropic quantum cosmologies: models with variable spatial curvature

Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they involve varying spatial curvature unlike the most talked about homogeneous but anisotropic cosmological models like Bianchi I, V and IX. We exhibit either an explicit example of the unitary solutions of the Wheeler–DeWitt equation, or at least show that a self-adjoint extension is possible.

Anisotropic string cosmological model in Brans–Dicke theory of gravitation with time-dependent deceleration parameter

We discuss a spatially homogeneous and anisotropic string cosmological models in the Brans–Dicke theory of gravitation. For a spatially homogeneous metric, it is assumed that the expansion scalar θ is proportional to the shear scalar σ. This condition leads to A = kBm, where k and m are constants. With these assumptions and also assuming a variable scale factor a = a(t), we find solutions of the Brans–Dicke field equations. Various phenomena like the Big Bang, expanding universe, and shift from anisotropy to isotropy are observed in the model. It can also be seen that in early stage of the evolution of the universe, strings dominate over particles, whereas the universe is dominated by massive strings at the late time. Some physical and geometrical behaviors of the models are also discussed and observed to be in good agreement with the recent observations of SNe la supernovae.

Local equilibrium solutions in simple anisotropic cosmological models, as described by relativistic fluid dynamics

We test the physical relevance of the full and the truncated versions of the Israel–Stewart (IS) theory of irreversible thermodynamics in a cosmological setting. Using a dynamical systems method, we determine the asymptotic future of plane symmetric Bianchi type I spacetimes with a viscous mathematical fluid, keeping track of the magnitude of the relative dissipative fluxes, which determines the applicability of the IS theory. We consider the situations where the dissipative mechanisms of shear and bulk viscosity are involved separately and simultaneously. It is demonstrated that the only case in the given model when the fluid asymptotically approaches local thermal equilibrium, and the underlying assumptions of the IS theory are therefore not violated, is that of a dissipative fluid with vanishing bulk viscosity. The truncated IS equations for shear viscosity are found to produce solutions which manifest pathological dynamical features and, in addition, to be strongly sensitive to the choice of initial conditions. Since these features are observed already in the case of an oversimplified mathematical fluid model, we have no reason to assume that the truncation of the IS transport equations will produce relevant results for physically more realistic fluids. The possible role of bulk and shear viscosity in cosmological evolution is also discussed.

Anisotropic solutions in f(R) gravity

Anisotropic cosmological models are investigated in the frame work of $f(R)$ gravity in the metric formalism. Plane symmetric models are considered to incorporate anisotropy in the expansion rates along different spatial directions. The anisotropy in expansion rates are assumed to be maintained throughout the cosmic evolution. Two accelerating models are constructed by considering different functional forms for f(R). The viability of these models are tested through a stability analysis.

Two-oscillator Kantowski–Sachs model of the Schwarzschild black hole interior

In this paper the interior of the Schwarzschild black hole, which is presented as a vacuum homogeneous and anisotropic Kantowski-Sachs minisuperspace cosmological model, is considered. Lagrangian of the model is reduced by a suitable coordinate transformation to Lagrangian of two decoupled oscillators with the same frequencies and with zero energy in total (an oscillator-ghost-oscillator system). The model will be presented in a classical, a p-adic and a noncommutative case. Then, within the standard quantum approach Wheeler-DeWitt equation and its general solutions, i.e. a wave function of the model, will be written, and then an adelic wave function will be constructed. Finally, thermodynamics of the model will be studied by using the Feynman-Hibbs procedure.

Nonlinear spinor field in isotropic space-time and dark energy models

Within the scope of isotropic FRW cosmological model the role of nonlinear spinor field in the evolution of the Universe is studied. It is found that unlike in anisotropic cosmological models in the present case the spinor field does not possess nontrivial non-diagonal components of energy-momentum tensor, consequently does not impose any additional restrictions on the components of the spinor field or metric function. The spinor description of different matter was given and evolution of the Universe corresponding to these sources is illustrated. In the framework of a three fluid system the utility of spinor description of matter is established.

Anisotropic cosmological models in f ( G ) $f(G)$ gravity

The main objective of this manuscript is to study the anisotropic universe in \(f(G)\) Gravity. For this purpose, locally rotationally symmetric Bianchi type \(I\) spacetime is considered. A viable \(f(G)\) model is used to explore the exact solutions of modified field equations. In particular, two families involving power law and exponential type solutions have been discussed. Some important cosmological parameters are calculated for the obtained solutions. Moreover, energy density and pressure of the universe is analyzed for the model under consideration.

Shear-free anisotropic cosmological models in $${\varvec{f}\,\varvec{(R)}}$$ f ( R ) gravity

We study a class of shear-free, homogeneous but anisotropic cosmological models with imperfect matter sources in the context of f(R) gravity. We show that the anisotropic stresses are related to the electric part of the Weyl tensor in such a way that they balance each other. We also show that within the class of orthogonal f(R) models, small perturbations of shear are damped, and that the electric part of the Weyl tensor and the anisotropic stress tensor decay with the expansion as well as the heat flux of the curvature fluid. Specializing in locally rotationally symmetric spacetimes in orthonormal frames, we examine the late-time behaviour of the de Sitter universe in $f(R)$ gravity. For the Starobinsky model of f(R), we study the evolutionary behavior of the Universe by numerically integrating the Friedmann equation, where the initial conditions for the expansion, acceleration and jerk parameters are taken from observational data.

An approach to investigate stability, cosmography and the dark energy dipole: A case study of cosmological models in R1+ϵ

In this paper, in a new approach, we study the stability of the dynamical system (DS) of [Formula: see text] in terms of two significant cosmological parameters, deceleration parameter and jerk parameter [Formula: see text]. Other cosmographic parameters such as [Formula: see text] have been obtained in terms of these two parameters. We have obtained critical points ([Formula: see text]), the best fitted current values of cosmographic parameters ([Formula: see text]), best value for model parameter [Formula: see text] and best trajectory of dynamics of system in phase space by simultaneously solving the DS and best fitting the parameter by the SNIa data. By defining modified redshift in anisotropic cosmological model as [Formula: see text] (where [Formula: see text] is a magnitude of anisotropy, [Formula: see text] is direction of privileged axis and [Formula: see text] is the direction of each SNe Ia sample to galactic coordinates), the luminosity distance has been obtained in terms of modified redshift using cosmography method. Using union 2 data, we have found the direction of privileged axis in the galactic coordinate. The results show that the magnitude of anisotropy is about [Formula: see text] and the direction of privileged axis is [Formula: see text]. Also, our results are consistent with other studies in [Formula: see text] confidence level.

Chameleon scalar field in LRS Bianchi type I cosmological model

We consider an anisotropic cosmological model with cold dark matter and a scalar field, where one component of the scale factor is taken in the framework of (i) a logamediate scenario (ii) an intermediate scenario, and (iii) an emergent scenario. In all cases we find expressions for the Chameleon field, Chameleon potential, the statefinder diagnostic pair, i.e., the {r, s} parameters, and the slow-roll parameters. All physical parameters are calculated and discussed in all three cases. It is also shown how the Chameleon field is directly affected by the role of curvature of space time. At large times (t→∞) the models tend asymptotically to an isotropic Friedmann–Robertson–Walker cosmological model.

Anisotropic Plane Symmetric Two-Fluid Cosmological Model with Time-Varying G and Λ

We investigate a two-fluid anisotropic plane symmetric cosmological model with variable gravitational constant G(t) and cosmological term Λ(t). In the two-fluid model, one fluid is chosen to be that of the radiation field modeling the cosmic microwave background and the other one a perfect fluid modeling the material content of the universe. Exact solutions of the field equations are obtained by using a special form for the average scale factor which corresponds to a specific time-varying deceleration parameter. The model obtained presents a cosmological scenario which describes an early acceleration and late-time deceleration. The gravitation constant increases with the cosmic time whereas the cosmological term decreases and asymptotically tends to zero. The physical and kinematical behaviors of the associated fluid parameters are discussed.

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.

Anisotropic cosmological models with bulk viscosity and particle creation in Saez–Ballester theory of gravitation

The paper deals with the study of particle creation and bulk viscosity in the evolution of spatially homogeneous and anisotropic Bianchi type-V cosmological models in the framework of Saez–Ballester theory of gravitation. Particle creation and bulk viscosity are considered as separate irreversible processes. The energy–momentum tensor is modified to accommodate the viscous pressure and creation pressure which is associated with the creation of matter out of gravitational field. A special law of variation of Hubble parameter is applied to obtain exact solutions of field equations in two types of cosmologies, one with power-law expansion and the other with exponential expansion. Cosmological model with power-law expansion has a Big-Bang singularity at time t = 0, whereas the model with exponential expansion has no finite singularity. We study bulk viscosity and particle creation in each model in four different cases. The bulk viscosity coefficient is obtained for full causal, Eckart’s and truncated theories. All physical parameters are calculated and thoroughly discussed in both models.

Anisotropic Bianchi Type-II Model with Cosmic Domain Walls in Self Creation Cosmology

The paper deals with a spatially homogeneous and totally anisotropic Bianchi type-II cosmological model in the presence of cosmic domain walls within the framework of Barber’s second self-creation theory of gravitation. Exact solutions of Einstein’s field equations are obtained by considering two ansatz: (i) the space–time admits a negative constant deceleration parameter and (ii) one of the components of the shear tensor is proportional to the mean Hubble parameter. The physical and geometrical aspects of the model are discussed.

Hamiltonian dynamics of space

The dynamics of space is considered as Hamiltonian dynamics. The general dynamic relations are derived in a synchronous coordinate system. As an example, the Hamiltonian dynamics of the Belinsky-Khalatnikov-Lifshitz anisotropic cosmological model is considered. The conditions of a smooth anisotropic exit from the point r = 0 are obtained. It is concluded that in general relativity there is the unnecessary constraint H = 0as a consequence of the principle of general covariance which follows from nowhere.

Unified dark fluid in Brans–Dicke theory

Anisotropic dark energy cosmological models are constructed in the frame work of generalised Brans-Dicke theory with a self interacting potential. Wet dark fluid characterized by a linear equation of state is considered as the source of dark energy. Shear scalar is considered to be proportional to the expansion scalar simulating an anisotropic relationship among the directional expansion rates. The dynamics of the universe in presence of wet dark fluid in anisotropic background have been discussed. The presence of evolving scalar field makes it possible to get accelerating phase of expansion even for a linear relationship among the directional Hubble rates. It is found that, the anisotropy in expansion rates does not affect the scalar field, self interacting potential but it controls the non-evolving part of the Brans- Dicke parameter.

Restoring unitarity in anisotropic quantum cosmological models

The present work shows that a properly chosen ordering of operators can restore unitarity in anisotropic quantum cosmological models. Bianchi V and Bianchi IX models with a perfect fluid are worked out. A transformation of coordinates takes the Hamiltonian to that of an inverse square potential which has equal deficiency indices; thus, a self-adjoint extension is possible. Although not clearly detected before, we show here that isotropic models are also apt to violate the conservation of probability for careless operator ordering.

Bulk Viscous Anisotropic Cosmological Models with Generalized Chaplygin Gas with Time Varying Gravitational and Cosmological Constants

This paper is devoted to studying the generalized Chaplygin gas models in Bianchi type III space- time geometry with time varying bulk viscosity, cosmological and gravitational constants. We are considering the condition on metric potential . Also to obtain deterministic models we have considered physically reasonable relations like , and the equation of state for generalized Chaplygin gas given by . A new set of exact solutions of Einstein’s field equations has been obtained in Eckart theory, truncated theory and full causal theory. Physical behaviour of the models has been discussed.