The Bianchi type III dark energy models with constant deceleration parameter are investigated. The equation of state parameter $ω$ is found to be time dependent and its existing range for this model is consistent with the recent observations of SN Ia data, SN Ia data (with CMBR anisotropy) and galaxy clustering statistics. The physical aspect of the dark energy models are discussed.
A spatially homogeneous anisotropic LRS Bianchi type-I cosmological model is studied in $f(R,T)$ gravity with a special form of Hubble's parameter, which leads to constant deceleration parameter. The parameters involved in the considered form of Hubble parameter can be tuned to match, our models with the $Λ$CDM model. With the present observed value of the deceleration parameter, we have discussed physical and kinematical properties of a specific model. Moreover, we have discussed the cosmological distances for our model.
The present study deals with LRS Bianchi type I cosmological model representing massive string. The energy-momentum tensor for such string as formulated by Letelier (1983) is used to construct massive string cosmological models for which we assume that the shear scalar ($σ$) is proportional to the expansion scalar ($θ$). The study reveals that massive strings dominate the early Universe. The strings eventually disappear from the Universe for sufficiently large time, which is in agreement with the current astronomical observations. Some physical and geometrical behaviour of models are also disc…
Locally rotationally symmetric (LRS) Bianchi Type I cosmological models are examined in the presence of dynamically anisotropic dark energy and perfect fluid. We assume that the dark energy (DE) is minimally interacting, has dynamical energy density, anisotropic equation of state parameter (EoS). The conservation of the energy-momentum tensor of the DE is assumed to consist of two separately additive conserved parts. A special law is assumed for the deviation from isotropic EoS, which is consistent with the assumption on the conservation of the energy-momentum tensor of the DE. Exact solutions…
This manuscript investigate the dark energy Bianchi type-I cosmological models in presence of generalized Chaplygin gas, variable gravitational and cosmological constants. In this manuscript, exact solutions of Einstein field equations are obtained under the assumption of time periodic varying deceleration parameter. The physical and dynamical behaviors of the models have been discussed with the help of graphical representations. Also we have discussed the stability and physical acceptability of the obtained solutions
A plane symmetric Bianchi I model is considered with constant deceleration parameter, $q=α-1$, where $α\geq0$. The model with $α=0$ violates the NEC throughout the evolution, and hence provides a physically unrealistic scenario. The model with $α\neq0$ obeys the NEC and WEC at late times, which shows that the models in this case can render a physical realistic cosmological scenario, though for a restricted period of time. It is also shown that the physical and kinematical behaviour of both models remain similar to an LRS Bianchi I model.
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 …
An LRS Bianchi I model is considered with constant deceleration parameter, $q=α-1$, where $α\geq0$ is a constant. The physical and kinematical behaviour of the models for $α=0$ and $α\neq0$ is studied in detail. The model with $α=0$ describes late time acceleration, but eternal inflation demands a violation of the NEC and WEC. The acceleration is caused by phantom matter which approaches a cosmological constant at late times. The solutions with a scalar field also show that the model is compatible with a phantom field only. A comparison with the observational outcomes indicates that the univer…
This paper deals with a spatially homogeneous and totally anisotropic Bianchi type-V cosmological model within the framework of self interacting Brans Dicke theory of gravity in the background of anisotropic dark energy (DE) with variable equation of state (EoS) parameter and constant deceleration parameter. Constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. EoS parameter ω and its existing range for the models is in good agreement with the most recent observational data. We notice that ω given by (37) i.e ω(t) = log(k1t) is more suitab…
This paper is devoted to investigate the exact solutions of Bianchi types I and V spacetimes in the context of f(R, T) gravity [1]. For this purpose, we found two exact solutions in each case by using assumption of constant deceleration parameter and the variation law of Hubble parameter. The obtained solutions correspond to two different models of this universe. The physical behavior of these models is also discussed.
We study Bianchi type $I$ cosmological model in the presence of magnetized anisotropic dark energy. The energy-momentum tensor consists of anisotropic fluid with anisotropic EoS $p=ωρ$ and a uniform magnetic field of energy density $ρ_B$. We obtain exact solutions to the field equations using the condition that expansion is proportional to the shear scalar. The physical behavior of the model is discussed with and without magnetic field. We conclude that universe model as well as anisotropic fluid do not approach isotropy through the evolution of the universe.
This paper is devoted to study the Bianchi type III model in the presence of anisotropic fluid in f(R) gravity. Exponential and power-law volumetric expansions are used to obtain exact solutions of the field equations. We discuss the physical behavior of the solutions and anisotropy behavior of the fluid, the expansion parameter and the model in future evolution of the universe.
It is investigated the behaviour of the ``constants'' $G,$ $c$ and $Λ$ in the framework of a perfect fluid LRS Bianchi I cosmological model. It has been taken into account the effects of a $c-$variable into the curvature tensor. Two exact cosmological solutions are investigated, arriving to the conclusion that if $q<0$ (deceleration parameter) then $G,$ $c$ are growing functions on time $t$ while $Λ$ is a negative decreasing function on time.
Spatially homogeneous and anisotropic Bianchi type $VI_0$ cosmological models with cosmological constant are investigated in the presence of anisotropic dark energy. We examine the effects of electromagnetic field on the dynamics of the universe and anisotropic behavior of dark energy. The law of variation of the mean Hubble parameter is used to find exact solutions of the Einstein field equations. We find that electromagnetic field promotes anisotropic behavior of dark energy which becomes isotropic for future evolution. It is concluded that the isotropic behavior of the universe model is see…
In this paper, we investigate the statefinder, the deceleration and equation of state parameters when universe is composed of generalized holographic dark energy or generalized Ricci dark energy for Bianchi I universe model. These parameters are found for both interacting as well as non-interacting scenarios of generalized holographic or generalized Ricci dark energy with dark matter and generalized Chaplygin gas. We explore these parameters graphically for different situations. It is concluded that these models represent accelerated expansion of the universe.
Intrinsic time-dependent invariants are constructed for classical, flat, homogeneous, anisotropic cosmology with a massless scalar material source. Invariance under the time reparameterization-induced canonical symmetry group is displayed explicitly.
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.
A spatially homogeneous and anisotropic Bianchi Type I universe has been studied with ω <-1 without Big Smash. It is demonstrated that if cosmic dark energy behaves like a fluid with equation of state p = ωρ (p and ρ being pressure and energy density respectively) as well as generalized chaplygin gas simultaneously, Big Rip or Big Smash problem does not arise even for equation of state parameter ω <-1 unlike other phantom models, here, the scale factor for Bianchi Type I universe is found regular for all time. The present model is derived by using law of variation of Hubble's parameter from Bi…
A new class of exact solutions of Einstein's field equations with perfect fluid for an LRS Bianchi type-I spacetime is obtained by using a time dependent deceleration parameter. We have obtained a general solution of the field equations from which three models of the universe are derived: exponential, polynomial and sinusoidal form respectively. The behaviour of these models of the universe are also discussed in the frame of reference of recent supernovae Ia observations.
We consider the dynamics of a Bianchi type I spacetime in the presence of dilaton and magnetic fields. The general solution of the Einstein-Maxwell dilaton field equations can be obtained in an exact parametric form. Depending on the numerical values of the parameters of the model there are three distinct classes of solutions. The time evolution of the mean anisotropy, shear and deceleration parameter is considered in detail and it is shown that a magnetic-dilaton anisotropic Bianchi type I geometry does not isotropize, the initial anisotropy being present in the universe for all times.
This paper is devoted to investigate the exact solutions of Bianchi type $I$ spacetime in the context of $f(R,T)$ gravity [1], where $f(R,T)$ is an arbitrary function of Ricci scalar $R$ and trace of the energy momentum tensor $T$. For this purpose, we find two exact solutions using the assumption of constant deceleration parameter and variation law of Hubble parameter. The obtained solutions correspond to two different models of the universe. The physical behaviour of these models is also discussed.
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.
LRS Bianchi type-I models have been studied in the cosmological theory based on Lyra's geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for variable deceleration parameter models of the universe. We have compared our models with those of Einstein's field theory with the cosmological term $Λ$. Our frame of reference is restricted to the recent Ia observations of supernovae. Some physical behaviour of the models is also examined in the presence of perfect fluids.
This paper is a study of the effects of anisotropic matter sources on the qualitative evolution of spatially homogenous cosmologies of Bianchi type VIII. The analysis is based on a dynamical system approach and makes use of an anisotropic matter family developed by Calogero and Heinzle which generalises perfect fluids and provides a measure of deviation from isotropy. Thereby the role of perfect fluid solutions is put into a broader context. The results of this paper concern the past and future asymptotic dynamics of locally rotationally symmetric solutions of type VIII with anisotropic matter…
The Bianchi type-I universe filled with dark energy from a wet dark fluid has been considered. A new equation of state for the dark energy component of the universe has been used. It is modeled on the equation of state $p=γ(ρ-ρ_\star)$ which can describe a liquid, for example water. The exact solutions to the corresponding field equations are obtained in quadrature form. The solution for constant deceleration parameter have been studied in detail for power-law and exponential forms both. The cases $γ=1$ and $γ=0$ have been also analysed.
Within the scope of an anisotropic Bianchi type-VI cosmological model we have studied the evolution of the universe filled with perfect fluid and dark energy. To get the deterministic model of Universe, we assume that the shear scalar $(σ)$ in the model is proportional to expansion scalar $(\vartheta)$. This assumption allows only isotropic distribution of fluid. Exact solution to the corresponding equations are obtained. The EoS parameter for dark energy as well as deceleration parameter is found to be the time varying functions. Using the observational data qualitative picture of the evoluti…
The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we consider spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields. The dynamics of models of Bianchi types I, II, and IX are completely described; the two most striking results are the following: (i) There exis…
Using the one-parameter internal symmetry group in the Bianchi type-I spacetime for cosmological models with a perfect fluid, we show that a system of coordinates exists in the associated internal space where two scale factors become equal. We find the general solution for an anisotropic model containing a perfect fluid with constant baryotropic index and investigate the asymptotic regimes. We obtain exact solutions for a set of anisotropic fluids which includes an anisotropic stiff fluid.
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 present a general study of the dynamical properties of Anisotropic Bianchi Universes in the context of Einstein General Relativity. Integrability results using Kovalevskaya exponents are reported and connected to general knowledge about Bianchi dynamics. Finally, dynamics toward singularity in Bianchi type VIII and IX universes are showed to be equivalent in some precise sence.
Bianchi type V matter filled universe with varying lambda in general relativity are investigated by using the law of variation for the generalized mean Hubble parameter. This yields the constant value of deceleration parameter and generates two types of solutions for the average scale factor one is of power law type and other is of exponential type. The cosmological constant is found to be a decreasing function of time, which is supported by results from recent type Ia supernovae observations. Also it has been found that cosmological constant affects entropy. Some physical and geometric behavi…
The general form of the anisotropy parameter of the expansion for Bianchi type-III metric is obtained in the presence of a single diagonal imperfect fluid with a dynamically anisotropic equation of state parameter and a dynamical energy density in general relativity. A special law is assumed for the anisotropy of the fluid which reduces the anisotropy parameter of the expansion to a simple form. The exact solutions of the Einstein field equations, under the assumption on the anisotropy of the fluid, are obtained for exponential and power-law volumetric expansions. The isotropy of the fluid, sp…
The present study deals with a spatially homogeneous and anisotropic Bianchi-II cosmological model representing massive strings. The energy-momentum tensor, as formulated by Letelier (1983), has been used to construct a massive string cosmological model for which the expansion scalar is proportional to one of the components of shear tensor. The Einstein's field equations have been solved by applying a variation law for generalized Hubble's parameter that yields a constant value of deceleration parameter in Bianchi-II space-time. A comparative study of accelerating and decelerating modes of the…
The anisotropic Bianchi type I in multi-scalar field cosmology is studied with a particular potential of the form $\rm V= V_0 e^{-\left[λ_1 ϕ_1 + \cdots + λ_n ϕ_n \right]}\,,$ which emerges as a condition between the time derivatives of their corresponding momenta. Using the Hamiltonian formalism for the inflation epoch with a quintessence framework we find the exact solutions for the Einstein-Klein-Gordon (EKG) system with different scenarios specified by the parameter $\rm λ^2= \sum_{i=1}^n λ_i^2$. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solve…
In this work, we study the effect of a magnetic field on the growth of cosmological perturbations. We develop a mathematical consistent treatment in which a perfect fluid and a uniform magnetic field evolve together in a Bianchi I universe. We then study the energy density perturbations on this background with particular emphasis on the effect of the background magnetic field. We develop a full relativistic solution which refines previous analysis in the relativistic limit, recovers the known ones in the Newtonian treatment with adiabatic sound speed, and it adds anisotropic effects to the rel…
I study the dynamical effects due to the Brans-Dicke scalar $ϕ$-field at the early stages of a supposedly anisotropic Universe expansion in the scalar-tensor cosmology of Jordan-Brans-Dicke. This is done considering the behaviour of the general solutions for the homogeneous model of Bianchi type VII in the vacuum case. I conclude that the Bianchi-VII$_0$ model shows an isotropic expansion and that its only physical solution is equivalent to a Friedman-Robertson-Walker spacetime whose evolution can, depending on the value of the JBD coupling constant, begin in a singularity and, after expanding…
In order to investigate if the anisotropy of the spacetime may induce future singularities at a finite value of the cosmic time on the evolution of cosmological models, we study vacuum and non-vacuum Bianchi type I spacetimes exhibiting such future singularities. We show that in the case of Kasner vacuum cosmologies the spacetime may rip itself apart in a finite time, and only in the direction corresponding to the unique scale factor which diverges at this finite value of the cosmic time. The other two directional scale factors and the average scale factor do not diverge and tend to zero at th…
We derive the metric for a Bianchi type I space-time with energy density that is dominated by that of a perfect fluid with equation of state $p=wρ$ and whose anisotropy is seeded by a fixed norm spacelike vector field. We solve for the evolution of perturbations about this space-time. In particular, the Jeans instability in an expanding flat Friedmann-Robertson-Walker universe is modified by the presence of the vector field so that energy density perturbations develop direction-dependent growth. We also briefly consider observational limits on the vector field vacuum expectation value, $m$. We…
The main purpose of the present paper is to investigate LRS Bianchi type I metric in the presence of perfect fluid and dark energy. In order to obtain a deterministic solution of the field equations we have assumed that, the two sources of the perfect fluid and dark energy interact minimally with separate conservation of their energy momentum tensors. The EoS parameter of the perfect fluid is also assumed to be constant. In addition to these we have used a special law of variation of Hubble parameter proposed by Berman that yields constant deceleration parameter. For two different values of th…
Evolution of an anisotropic universe described by a Bianchi type I (BI) model in presence of nonlinear spinor field has been studied by us recently in a series of papers. On offer the Bianchi models, those are both inhomogeneous and anisotropic. Within the scope of Bianchi type VI (BVI) model the self-consistent system of nonlinear spinor and gravitational fields are considered. The role of inhomogeneity in the evolution of spinor and gravitational field is studied.
In one-loop string effective action, we study a generality of non-singular cosmological solutions found in the isotropic and homogeneous case. We discuss Bianchi I and IX type spacetimes. We find that nonsingular solutions still exist in Bianchi I model around nonsingular flat Friedmann solutions. On the other hand, we cannot find any nonsingular solutions in Bianchi IX model. Non-existence of nonsingular Bianchi IX universe may be consistent with the analysis by Kawai, Sakagami and Soda, i.e. the tensor mode perturbations against nonsingular flat Friedmann universe are unstable, because Bianc…
We analyze the global dynamics of Bianchi type I solutions of the Einstein equations with anisotropic matter. The matter model is not specified explicitly but only through a set of mild and physically motivated assumptions; thereby our analysis covers matter models as different from each other as, e.g., collisionless matter, elastic matter and magnetic fields. The main result we prove is the existence of an `anisotropy classification' for the asymptotic behaviour of Bianchi type I cosmologies. The type of asymptotic behaviour of generic solutions is determined by one single parameter that desc…
Cosmic Microwave Background anomalies suggest that the Universe is slightly anisotropic, so a Cosmological Model that does not satisfy the Cosmological Principle is necessary. Anisotropic Bianchi models have been studied given that they would be necessary to understand the early stages of the Universe. In this paper, we analyze qualitatively the behavior of the cosmological redshift in a Bianchi type I model after a coordinate transformation in three cases: vacuum with no vanishing cosmological constant $Λ\not= 0$, universe dominated by dust and universe dominated by radiation.
In this article we compute the density of Dirac particles created by a cosmological anisotropic Bianchi I universe in the presence of a constant electric field. We show that the particle distribution becomes thermal when one neglects the electric interaction.
In this paper, the cosmic no hair theorem for anisotropic Bianchi models which admit inflation with a scalar field is studied in the framework of Brane world. It is found that all Bianchi models except Bianchi type IX, transit to an inflationary regime with vanishing anisotropy. In the Brane world, anisotropic universe approaches the inflationary era much faster than that in the general theory of relativity. The form of the potential does not affect the evolution in the inflationary epoch. However, the late time behaviour is controlled by a constant additive factor in the potential for the inf…
In the context of modified tele-parallel theory of gravity, we undertake cosmological anisotropic models and search for their solutions. Within a suitable choice of non-diagonal tetrads, the decoupled equations of motion are obtained for Bianchi-I, Bianchi-III and Kantowski-Sachs models, from which we obtain the correspondent solutions. By the way, energy density and pressures are also obtained, showing, as an important result, that our universe may live a quintessence like universe even still anisotropic models are considered.
Some features of the Bianchi type-I universes in the presence of a fluid that wields an anisotropic equation of state (EoS) parameter are discussed in the context of general relativity. The models that exhibit de Sitter volumetric expansion due to the constant effective energy density (the sum of the energy density of the fluid and the anisotropy energy density) are of particular interest. We also introduce two locally rotationally symmetric models, which exhibit de Sitter volumetric expansion in the presence of a hypothetical fluid that has been obtained by minimally altering the conventional…
We solve the Wheeler-DeWitt equation for the minisuperspace of a cosmological model of Bianchi type I with a minimally coupled massive scalar field $ϕ$ as source by generalizing the calculation of Lukash and Schmidt [1]. Contrarily to other approaches we allow strong anisotropy. Combining analytical and numerical methods, we apply an adiabatic approximation for $ϕ$, and as new feature we find a period-doubling bifurcation. This bifurcation takes place near the cosmological quantum boundary, i.e., the boundary of the quasiclassical region with oscillating $ψ$-function where the WKB-approximatio…
The objective of this work enclosed with the study of spatially homogeneous anisotropic Bianchi type-I universe in $f(R,T)$ gravity (where $R$ is the Ricci scalar and $T$ is the trace of stress energy momentum tensor) in two different cases viz. $f(R,T)=R+2f(T)$ and $f(R,T)=f_1(R)+f_2(T)$ with bulk viscosity matter content. In this study, we consider a time varying deceleration parameter, which generates an accelerating universe to obtain the exact solution of the field equations. The physical and kinematical properties of both the models are discussed in detail for the future evolution of the…
The dynamics of Dvali-Gabadadze-Porrati Cosmology (DGP) braneworld with an anisotropic brane is studied. The Friedmann equations and their solutions are obtained for two branches of anisotropic DGP model. The late time behavior in DGP cosmology is examined in the presence of anisotropy which shows that universe enters a self-accelerating phase much later compared to the isotropic case. The acceleration conditions and slow-roll conditions for inflation are obtained.
In this article we compute the density of scalar and Dirac particles created by a cosmological anisotropic Bianchi type I universe in the presence of a time varying electric field. We show that the particle distribution becomes thermal when one neglects the electric interaction.
Using scaled variables we are able to integrate an equation valid for isotropic and anisotropic Bianchi type I, V, IX models in Brans-Dicke (BD) theory. We analyze known and new solutions for these models in relation with the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. In particular, a new solution of curve ($k\neq0$) Friedmann-Robertson-Walker (FRW) cosmologies in Brans-Dicke theory is analyzed.
The paper deals with Bianchi type V Universe, which has dynamical energy density. We consider Bianchi type V space-time, introducing three different skewness parameters along spatial directions to quantify the deviation of pressure from isotropy. To study the anisotropic nature of the dynamical dark energy, we assume that the skewness parameters are time dependent. It is found that the Universe achieves flatness in quintessence model. The physical behavior of the Universe has been discussed in detail.
Despite having the somewhat successful description of accelerated cosmology, the early evolution of the universe always challenges mankind. Our promising approach lies in a new class of symmetric teleparallel theory of gravity named $f(Q)$, where the non-metricity scalar $Q$ is responsible for the gravitational interaction, which may resolve some of the issues. To study the early evolution of the universe, we presume an anisotropic locally rotationally symmetric (LRS) Bianchi-I spacetime and derive the motion equations. We discuss the profiles of energy density, equation of state and skewness …
Spatially homogeneous but totally anisotropic and non-flat Bianchi type II cosmological model has been studied in general relativity in the presence of two minimally interacting fluids; a perfect fluid as the matter fluid and a hypothetical anisotropic fluid as the dark energy fluid. The Einstein's field equations have been solved by applying two kinematical ansätze: we have assumed the variation law for the mean Hubble parameter that yields a constant value of deceleration parameter, and one of the components of the shear tensor has been considered proportional to the mean Hubble parameter. W…
