We investigate the behaviour on approach to the initial singularity in higher-order extensions of general relativity by finding exact cosmological solutions for a wide class of models in which the Lagrangian is allowed to depend nonlinearly upon the three possible linear and quadratic scalars built from the Riemann tensor; $R$, $R_{ab}R^{ab}$ and $R_{abcd}R^{abcd}$. We present new anisotropic vacuum solutions analagous to the Kasner solutions of general relativity and extend previous results to a much wider range of fourth order theories of gravity. We discuss the implications of these results for the behaviour of the more general anisotropic Bianchi type VIII and IX cosmologies as the initial singularity is approached. Furthermore, we also consider the existence conditions for some other simple anisotropic Bianchi I vacuum solutions in which the expansion in each direction is of exponential, rather than power-law behaviour and their relevance for cosmic ``no-hair'' theorems.
We write down an anisotropic solution for a flat 5+1 dimensional Universe in Gauss-Bonnet gravity. In the model under investigation this solution replaces the generalized Kasner solution near a cosmological singularity.
Tunneling rate is investigated in homogenous and anisotropic cosmologies. The calculations is done by two methods: Euclidean and Hamiltonian approaches. It is found that the probability decreases exponentialy as anisotropy is increased.
The braneworld cosmological model was constructed by embedding a 3-brane into a higher dimensional bulk background geometry and the usual matter of our universe was assumed to be confined in the brane while the gravity can propagate in the bulk. By considering that the bulk geometry is anisotropic, after reviewed the separable solution for the bulk metric and the result that the anisotropic property of the bulk can support the perfect fluid kind of the matter in the brane, we develop a formalism of the cosmological perturbation for this kind of anisotropic braneworld model. As in isotropic cas…
Anisotropic Bianchi-III cosmological model is investigated with variable gravitational and cosmological constants in the framework of Einstein's general relativity. The shear scalar is considered to be proportional to the expansion scalar. The dynamics of the anisotropic universe with variable G and Lambda are discussed. Without assuming any specific forms for Lambda and the metric potentials, we have tried to extract the time variation of G and Lambda from the anisotropic model. The extracted G and Lambda are in conformity with the present day observation. Basing upon the observational limits…
In the present work, we discuss the Wheeler-DeWitt quantization scheme for an n-dimensional anisotropic cosmological model with a perfect fluid in presence of a massless scalar field. We identify the time parameter using the generalization of Schutz formalism and find the wavepacket of the universe following standard Wheeler-DeWitt methodology of quantum cosmology. We also calculate the expectation values of scale factors and volume element. We show that quantized model escapes the singularity and supports bouncing universe solutions.
We present new solutions of the string cosmological effective action in the presence of a homogeneous Maxwell field with pure magnetic component. Exact solutions are derived in the case of space-independent dilaton and vanishing torsion background. In our examples the four dimensional metric is either of Bianchi-type III and VI$_{-1}$ or Kantowski-Sachs.
The anisotropic Bianchi I cosmological model coupled with perfect fluid is quantized in the minisuperspace. The perfect fluid is described by using the Schutz formalism which allows to attribute dynamical degrees of freedom to matter. It is shown that the resulting model is non-unitary. This breaks the equivalence between the many-worlds and dBB interpretations of quantum mechanics.
A class of exact solutions for the Einstein-Maxwell field equations are obtained by assuming the erstwhile cosmological constant $ Λ$ to be a space-variable scalar, viz., $ Λ=Λ(r) $. The source considered here is static, spherically symmetric and anisotropic charged fluid. The solutions obtained are matched continuously to the exterior Reissner-Nordström solution and each of the four solutions represents an electromagnetic mass model.
We consider the cosmological evolution of a flat anisotropic Universe in $f(T)$ gravity in the presence of a perfect fluid. It is shown that the matter content of the Universe has a significant impact of the nature of a cosmological singularity in the model studied. Depending on the parameters of the $f(T)$ function and the equation of state of the perfect fluid in question the well-known Kasner regime of general relativity can be replaced by a new anisotropic solution, or by an isotropic regime, or the cosmological singularity changes its nature to a non-standard one with a finite values of H…
Exact electromagnetic wave solutions to Maxwell equations on anisotropic Bianchi I cosmological spacetime backgrounds are studied. The waves evolving on Bianchi I spacetimes exhibit birefringence (associated to linear polarization) and dispersion. The particular case of a vacuum--dominated anisotropic Universe, which reproduces a Friedmann-Robertson-Walker Universe (for late times) while for earlier times it matches a Kasner Universe, is studied. The electromagnetic waves do not, in general, follow null geodesics. This produces a modification of the cosmological redshift, which is now dependen…
The article is devoted to cosmology. It deals with homogeneous anisotropic cosmological models. Scale factors have been evaluated for the multicomponent models with perfect fluid, taking account of its expansion, rotation and shear. The cosmological fluid components are as follows: phantom matter, de Sitter vacuum, domain walls, strings, dust, radiation, perfect gas, stiff matter and ekpyrotic matter. The scale factor dependences on the equation of state and kinematic invariants of the perfect fluid have been analysed. The paper is aimed at finding exact solutions of Friedmann and Raychaudhuri…
In this work a class of interior solution for Einstein field equations corresponding to a spherically symmetric anisotropic fluid sphere has been obtained under the assumption that the cosmological constant is spatially variable. The solution obtained has the characteristics that the pressure and the cosmological parameter vanish at the centre and at the boundary with a maximum value somewhere inside the body. It has been argued that a variable $ Λ$ is as much important physically in Astrophysics as in Cosmology.
The gravitation theory is modified on the base of geometric identity and equivalence principle. This makes it possible to generalize the geodesics and solve several problems of classical GRT such as flat rotation curves of the spiral galaxies, Tully-Fisher law and some others and reveal the fundamental (geometrical) origin of the cH acceleration value. The developed approach contains all the results of the classical GRT and has promising cosmological consequences.
Static spherically symmetric anisotropic source has been studied for the Einstein-Maxwell field equations assuming the erstwhile cosmological constant $ Λ$ to be a space-variable scalar, viz., $ Λ= Λ(r) $. Two cases have been examined out of which one reduces to isotropic sphere. The solutions thus obtained are shown to be electromagnetic in origin as a particular case. It is also shown that the generally used pure charge condition, viz., $ ρ+ p_r = 0 $ is not always required for constructing electromagnetic mass models.
In this paper, we have investigated some accelerating cosmological models at the backdrop of an anisotropic metric in an extended gravity theory. Two viable cosmological models one with a little rip behaviour and the other with a hyperbolic form of Hubble parameter have been constructed. The dynamical aspects of the models along with some physical and geometrical parameters are analysed. Both the models presented here evolve in the phantom-like region and overlap with $Λ$CDM model at late times. We carried out a geometrical diagnosis of the model to show the viability of the models.
The main purpose of this paper is to explore the solutions of Bianchi type $III$ cosmological model in Brans Dicke theory of gravity in the background of anisotropic dark energy. We use the assumption of constant deceleration parameter and power law relation between scalar field $ϕ$ and scale factor $a$ to find the solutions. The physical behavior of the solutions has been discussed using some physical quantities.
Recently the small value of the cosmological constant and its ability to accelerate the expansion of the Universe is of great interest. We discuss the possibility of forming of anisotropic compact stars from this cosmological constant as one of the competent candidates of dark energy. For this purpose we consider the analytical solution of Krori and Barua metric. We take the radial dependence of cosmological constant and check all the regularity conditions, TOV equations, stability and surface redshift of the compact stars. It has been shown as conclusion that this model is valid for any compa…
We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy given by a cosmological constant. The perfect fluid is chosen to be the one obeying either the usual equation of state, i.e., $p = ζ\ve$, with $ζ\in [0, 1]$ or a van der Waals equation of state. Role of the $Λ$ term in the evolution of the BI Universe has been studied.
Here, we have investigated the interaction of Bianchi type I anisotropic cloud string cosmological model universe with electromagnetic field in the context of general relativity. In this paper, the energy momentum tensor is assumed to be the sum of the rest energy density and string tension density with an electromagnetic field. To obtain exact solutions of Einstein field equations, we take average scale factor as an integrating function of time. Also, the dynamics and significance of various physical parameters of model are discussed.
We consider a particular example of dynamical compactification of an anisotropic 7+1 dimensional Universe in Einstein - Gauss - Bonnet gravity. Starting from rather general totally anisotropic initial conditions a Universe in question evolves towards a product of two isotropic subspaces. The first subspace expands isotropically, the second represents an "inner" isotropic subspace with stabilized size. The dynamical evolution does not require fine-tuning of initial conditions, though it is possible for a particular range of coupling constants. The corresponding condition have been found analyti…
Were studied classical oscillations of background metric in the multidimensional anisotropic model of Kazner in the de-Sitter stage. Obtained dependence of fluctuations on dimension of space-time with infinite expansion. Stability of the model could be achieved when number of space-like dimensions equals or more then four. Were calculated contributions to the density of "vacuum energy", that are providing by proper oscillations of background metric and compared with contribution of cosmological arising of particles due to expansion. As it turned out, contribution of gravitational oscillation o…
Bianchi type I magnetized cosmological models in the presence of a bulk viscous fluid are investigated. The source of the magnetic field is due to an electric current produced along x-axis. The distribution consists of an electrically neutral viscous fluid with an infinite electrical conductivity. The coefficient of bulk viscosity is assumed to be a power function of mass density. The cosmological constant $Λ$ is found to be positive and is a decreasing function of time which is supported by results from recent supernovae observations. The behaviour of the models in presence and absence of mag…
We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., $p = ζ\ve$, with $ζ\in [0, 1]$ whereas, the dark energy density is considered to be either the quintessence or the Chaplygin gas. Exact solutions to the corresponding Einstein equations are obtained.
Cosmological solutions are obtained in an anisotropic Kantowski-Sachs (KS) and Bianchi Type-I universes considering a cosmological constant with Skyrme fluid. Interestingly, the solutions obtained here in both the KS and Bianchi-I anisotropic universes are found isotropize at late time due to the presence of the Skyrme fluid even in the absence of $Λ$ term or any inflationary mechanism involving the inflaton field. A comparative study of both the anisotropic cosmological models are carried out here and found that Bianchi-I universe admits oscillatory solutions for a given matter configuration.…
The dynamical features of Bianchi type $VI_h$ $(BVI_h)$ universe are investigated in $f(R,T)$ theory of gravity. The field equations and the physical properties of the model are derived considering a power law expansion of the universe. The effect of anisotropy on the dynamics of the universe as well on the energy conditions are studied. The assumed anisotropy of the model is found to have substantial effects on the energy condition and dynamical parameters.
Among the general class of metric-affine theories of gravity, there is a special class conformed by those endowed with a projective symmetry. Perhaps the simplest manner to realise this symmetry is by constructing the action in terms of the symmetric part of the Ricci tensor. In these theories, the connection can be solved algebraically in terms of a metric that relates to the spacetime metric by means of the so-called deformation matrix that is given in terms of the matter fields. In most phenomenological applications, this deformation matrix is assumed to inherit the symmetries of the matter…
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 orthon…
In the present work we have searched the existence of the late time acceleration of the universe with string fluid as source of matter in anisotropic Heckmann-Suchking space-time by using 287 high red shift $(0.3 \leq z\leq 1.4)$ SN Ia data of observed absolute magnitude along with their possible error from Union 2.1 compilation. It is found that the best fit values for $(Ω_{m})_{0}$, $(Ω_Λ)_{0}$, $(Ω_σ)_{0}$ and $(q)_{0}$ are 0.2820, 0.7177, 0.0002 $\&$ -0.5793 respectively. Several physical aspects and geometrical properties of the model are discussed in detail.
The paper presents some exact solutions of Bianchi types I, III and Kantowski-Sachs cosmological models consisting of a dissipative fluid along with an axial magnetic field. A barytropic equation of state between the thermodynamic pressure and the matter density, together with a pair of linear relations between the matter density, the shear scalar, and the expansion scalar have been assumed for simplicity. The solutions are basically of two different types, one for the Bianchi-I and the other for Bianchi-III and Kantowski-Sachs type. The presence of the magnetic field, however, does not change…
In the present article we analyze the phenomenon of particle creation in a cosmological anisotropic universe when a constant electric field is present. We compute, via the Bogoliubov transformations, the density number of particles created.
A Bianchi type -I metric of Kasner form is considered, when the space is filled with a viscous fluid. Whereas an ideal (nonviscous) fluid permits the Kasner metric to be anisotropic provided that the fluid satisfies the Zel'dovich equation of state, the viscous fluid does not permit the Kasner metric to be anisotropic at all. In the latter case, we calculate the Kasner (isotropic) metric expressed by the fluid's density, pressure, and bulk viscosity, at some chosen instant $t=t_0$. The equation of state is also calculated. The present paper is related to a recent Comment of Cataldo and del Cam…
In this note I discuss the problem of cosmological singularities within gauge theories of gravitation. Solutions of cosmological equations with the scalar field are considered.
In this paper, aniostropic dark energy cosmological models have been constructed in a Bianchi-V space-time with the energy momentum tensor consisting of two non-interacting fluids namely bulk viscous fluid and dark energy fluid. Two different models are constructed based on the power law cosmology and de Sitter universe. The constructed model also embedded with different pressure gradients along different spatial directions. The variable equation of state (EoS) parameter, skewness parameters for both the models are obtained and analyzed. The physical properties of the models obtained with the …
The truncated Israel-Stewart theory of irreversible thermodynamics is used to describe the bulk viscous pressure and the anisotropic stress in a class of spatially homogeneous viscous fluid cosmological models. The governing system of differential equations is written in terms of dimensionless variables and a set of dimensionless equations of state is utilized to complete the system. The resulting dynamical system is then analyzed using standard geometric techniques. It is found that the presence of anisotropic stress plays a dominant role in the evolution of the anisotropic models. In particu…
Anisotropic exponential cosmological solutions for a space of arbitrary dimension filled with ordinary matter in the 4th and 5th orders of Lovelock gravity are obtained. Also we have supposed a generalization of such solutions on an arbitrary order. All the solutions are represented as a set of conditions on Hubble parameters.
The theory of cosmological perturbations is extended to spacetimes displaying isotropic expansion but anisotropic curvature. The perturbed Einstein equation and Boltzmann equations for massless and massive particles are derived in a general gauge and a decomposition of perturbations into harmonic modes and moments is proposed. Generalization to the case where anisotropic expansion is also present in the background is discussed.
Given an anisotropic fluid source, we determine in closed forms, upon solving the field equations of general relativity (GR) and teleparallel gravity (TEGR) coupled to a cosmological constant, cylindrically symmetric four-dimensional cosmological rotating wormholes, satisfying all local energy conditions, and cosmological rotating solutions with two axes of symmetry at finite proper distance. These solutions have the property that their angular velocity is proportional to the cosmological constant.
We use the Sáez-Ballester theory on anisotropic Bianchi I cosmological model, with barotropic fluid and cosmological constant. We obtain the classical solution by using the Hamilton-Jacobi approach. Also the quantum regime is constructed and exact solutions to the Wheeler-DeWitt equation are found.
We describe Lemaître-Tolman-Bondi cosmological models where an anisotropic pressures is considered. By using recent astronomical observations coming from supernova of Ia types we constraint the values of the parameters that characterize our models.
We investigate anisotropic cosmological solutions of the theory with non-minimal couplings between electromagnetic fields and gravity in $Y(R) F^2$ form. After we derive the field equations by the variational principle, we look for spatially flat cosmological solutions with magnetic fields or electric fields. Then we give exact anisotropic solutions by assuming the hyperbolic expansion functions. We observe that the solutions approach to the isotropic case in late-times.
The study of a self-consistent system of nonlinear spinor and Bianchi type I gravitational fields in presence of a viscous fluid and $Λ$ term with the spinor field nonlinearity being some arbitrary functions of the invariants $I$ an $J$ constructed from bilinear spinor forms $S$ and $P$, generates a multi-parametric system of ordinary differential equations \cite{saharrp,grqcnlsp}. A qualitative analysis of the system in question has been thoroughly carried out. A complete qualitative classification of the mode of evolution of the universe given by the corresponding dynamic system has been ill…
Motion of an ultra-relativistic perfect fluid in space-time with the Kasner metrics is investigated by the Hamiltonian method. It is found that in the limit of small times a tendency takes place to formation of strong inhomogeneities in matter distribution. In the case of slow flows the effect of non-stationary anisotropy on dynamics of sound waves and behaviour of frozen-in vortices is considered. It is shown that hydrodynamics of slow vortices on the static homogeneous background is equivalent to the usual Eulerian incompressible hydrodynamics, but in the presence of an external non-stationa…
An effective time--dependent cosmological constant can be recovered for higher--order theories of gravity by extending to these ones the no--hair conjecture. The results are applied to some specific cosmological models.
We show that the inclusion of a term $C_{abcd}C^{abcd}$ in the action can remove the recently described anisotropic singularity occurring on the hypersurface $F(ϕ)=0$ of scalar-tensor theories of gravity of the type $$ S=\int d^4x \sqrt{-g} {F(ϕ)R - \partial_aϕ\partial^aϕ-2V(ϕ)}, $$ preserving, by construction, all of their isotropic solutions. We show that, in principle, a higher order term of this type can arise from considerations about the renormalizability of the semiclassical approach to the theory. Such result brings again into consideration the quintessential models recently proposed b…
In this work, the cosmological implications of brane world scenario are investigated when the gravitational coupling $G$ and the cosmological term $Λ$ are not constant but rather there are time variation of them. From observational point of view, these time variations are taken in the form $\frac{\dot{G}}{G}\sim H$ and $Λ\sim H^{2}$. The behavior of scale factors and different kinematical parameters are investigated for different possible scenarios where the bulk cosmological constant $Λ_{5}$ can be zero, positive or negative.
We study the evolution of cosmological event horizons in anisotropic Kasner universes in the presence of a positive cosmological constant by analyzing null geodesics. At later times, the asymptotic form of cosmological horizons is the same spherical surface as the de Sitter horizon. At the early times, however, it has non-spherical shape with its eccentricity decreases with time. The horizon area increases with time respecting the second law of thermodynamics. The initial shape of the cosmological horizon takes the form of a needle or pancake surface depending on the nature of the background s…
We perform dynamical analysis of anisotropic Rastall cosmologies and, in particular Kantowski-Sachs, locally rotationally symmetric (LRS) Bianchi I and LRS Bianchi III cosmologies. Using dynamical system techniques, a qualitative analysis of cosmological equations yield physically interesting cases which are in agreement with observations such as de Sitter, accelerating, stable attractors are isotropic. Features such as isotropization and cosmological bounce are discussed in detail.
We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., $p = ζ\ve$, with $ζ\in [0, 1]$ whereas, the dark energy is considered to be obeying a quintessence-like equation of state. Exact solutions to the corresponding Einstein equations are obtained. The model in consideration gives rise to a Universe which is spatially finite. Depending on the choice of problem parameters the Universe is either close with a space-time singularity, or …
We present an exact solution of Einstein equations that describes a Bianchi type III spacetime with conformal expansion. The matter content is given by an anisotropic scalar field and two perfect fluids representing dust and isotropic radiation. Based on this solution, we construct a cosmological model that respects the evolution of the scale factor predicted in standard cosmology.
In this work, we study a cosmological model of Bianchi type-I Universe in teleparallel gravity for a perfect fluid. To obtain the cosmological solution of the model, we assume that the deceleration parameter is a linear function of the Hubble parameter $H$ i.e. $q=-1+βH$ (where $β$ as a positive constant). Consequently, we get a model of our Universe, where it goes from the initial phase of deceleration to the current phase of acceleration. We have discussed some physical and geometric properties such as Hubble parameter, deceleration parameter, energy density, pressure, and equation of state …
Recent released Planck data and other astronomical observations show that the universe may be anisotropic on large scales. This hints a cosmological privileged axis in our anisotropic expanding universe. This paper proceeds a modified redshift in anisotropic cosmological model as $ 1+\tilde{z}(t,\hat{\textbf{p}})=\frac{a(t_{0)}}{a(t)}(1-A(\hat{\textbf{n}}.\hat{\textbf{p}}))$ (where $A$ is the magnitude of anisotropy ,$\hat{\textbf{n}}$ is the direction of privileged axis, and $\hat{\textbf{p}}$ is the direction of each SNe Ia sample to galactic coordinates) along with anisotropic parameter $δ=…
In the framework of extended gravity theories, we discuss the meaning of a time dependent "cosmological constant" and give a set of conditions to recover asymptotic de Sitter behaviour for a class of cosmological models independently of initial data. To this purpose we introduce a time-dependent (effective) quantity which asymptotically becomes the true cosmological constant. We will deal with scalar-tensor, fourth and higher than fourth-order theories.
The study of a self-consistent system of interacting spinor and scalar fields within the scope of a Bianchi type I (BI) gravitational field in presence of a viscous fluid and $Λ$ term has been carried out. The system of equations defining the evolution of the volume scale of BI universe, energy density and corresponding Hubble constant has been derived. The system in question has been thoroughly studied qualitatively. Corresponding solutions are graphically illustrated. The system in question is also studied from the view point of blow up. It has been shown that the blow up takes place only in…
