An LRS Bianchi-I space-time model is studied with constant Hubble parameter in $f(R,T)=R+2λT$ gravity. Although a single (primary) matter source is considered, an additional matter appears due to the coupling between matter and $f(R,T)$ gravity. The constraints are obtained for a realistic cosmological scenario, i.e., one obeying the null and weak energy conditions. The solutions are also extended to the case of a scalar field (normal or phantom) model, and it is found that the model is consistent with a phantom scalar field only. The coupled matter also acts as phantom matter. The study shows that if one expects an accelerating universe from an anisotropic model, then the solutions become physically relevant only at late times when the universe enters into an accelerated phase. Placing some observational bounds on the present equation of state of dark energy, $ω_0$, the behavior of $ω(z)$ is depicted, which shows that the phantom field has started dominating very recently, somewhere between $0.2\lesssim z\lesssim0.5$.
In this paper we present the quantum LRS Bianchi IX models or, as they may be better known, the Taub-NUT models in addition to the quantum LRS Bianchi VIII models, both coupled to a stiff matter source. We solve their Wheeler DeWitt equations for an arbitrary Hartle-Hawking ordering parameter using separation of variables. Afterwards we construct a superposition of their respective wave functions and discuss some of the interesting qualitative properties they possess.
The aim of this paper is to explore teleparallel conformal Killing vector fields (CKVFs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes in the context of teleparallel gravity and compare the obtained results with those of general relativity. The general solution of teleparallel conformal Killing's equations is found in terms of some unknown functions of t and x , along with a set of integrability conditions. The integrability conditions are solved in some particular cases to get the final form of teleparallel CKVFs. It is observed that the LRS Bianchi type V spacetimes admit…
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.
An LRS Bianchi type-V cosmological models representing a viscous fluid distribution with a time dependent cosmological term $Λ$ is investigated. To get a determinate solution, the viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. It turns out that the cosmological term $Λ(t)$ is a decreasing function of time, which is consistent with recent observations of type Ia supernovae. Various physical and kinematic features of these models have also been explored.
In this paper we have investigated an LRS Bianchi I anisotropic cosmological model of the universe by taking time varying $G$ and $Λ$ in the presence of bulk viscous fluid source described by full causal non-equilibrium thermodynamics. We obtain a cosmological constant as a decreasing function of time and for $m, n > 0$, the value of cosmological ``constant'' for this model is found to be small and positive which is supported by the results from recent supernovae observations.
The general solution of the field equations in LRS Bianchi-I space-time with perfect fluid equation-of-state (EoS) is presented. The models filled with dust, vacuum energy, Zel'dovich matter and disordered radiation are studied in detail. A unified and systematic treatment of the solutions is presented, and some new solutions are found. The dust, stiff matter and disordered radiation models describe only a decelerated universe, whereas the vacuum energy model exhibits a transition from a decelerated to an accelerated phase.
In this paper we study the evolution of a LRS Bianchi I Universe, filled with a bulk viscous cosmological fluid in the presence of time varying constants "but" taking into account the effects of a c-variable into the curvature tensor. We find that the only physical models are those which ``constants'' $G$ and $c$ are growing functions on time $t$, while the cosmological constant $Λ$ is a negative decreasing function. In such solutions the energy density obeys the ultrastiff matter equation of state i.e. $ω=1$.
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.
Within the scope of Bianchi type-I cosmological model the role of spinor field on the evolution of the Universe is investigated. In doing so we have considered a polynomial type of nonlinearity. It is found that depending on the sign of self-coupling constant the model allows either accelerated mode of expansion or oscillatory mode of evolution. Unlike general Bianchi type-I and Bianchi type $VI_0$ models in this case neither mass term nor the nonlinear term in the Lagrangian of spinor field vanish.
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.
In this paper we report on results in the study of spatially homogeneous cosmological models with elastic matter. We show that the behavior of elastic solutions is fundamentally different from that of perfect fluid solutions already in the case of locally rotationally symmetric (LRS) Bianchi type I models; this is true even when the elastic material resembles a perfect fluid very closely. In particular, the approach to the initial singularity is characterized by an intricate oscillatory behavior of the scale factors, while the future asymptotic behavior is described by isotropization rates tha…
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…
Within the scope of a LRS Bianchi type-I cosmological model we study the role of the nonlinear spinor field in the evolution of the Universe. In doing so we consider a polynomial type of nonlinearity that describes different stages of the evolution. Finally we also use the observational data to fix the problem parameters that match best with the real picture of the evolution. The assessment of the age of the Universe in case of the soft beginning of expansion (initial speed of expansion in a point of singularity is equal to zero) the age was found 15 billion years, whereas in case of the hard …
We analyze the dynamics of a class of cosmological solutions of the Einstein-Vlasov equations. These equations describe an ensemble of collisionless particles (which represent galaxies or clusters of galaxies) that interact gravitatively through Einstein's equations of general relativity. The cosmological models we consider are spatially homogeneous, of Bianchi type IX, and locally rotationally symmetric (LRS). We prove that generic solutions exhibit an oscillatory approach toward the singularities (the "big bang" in the past and the "big crunch" in the future); this is in contrast to the beha…
We have studied the locally rotationally symmetric (LRS) Bianchi type-I cosmological model in $f(R,T)$ gravity ($R$ is the Ricci scalar and $T$ is the trace of the stress energy tensor) with Bulk viscous fluid as matter content. The model is constructed for the linear form $f(R,T)=R+2f(T)$. The exact solution of field equations is obtained by using a time varying deceleration parameter $q$ for a suitable choice of the function $f(T)$. In this work, the bulk viscous pressure $\bar{p}$ is found to be negative and energy density $ρ$ is found to be positive. The obtained model is anisotropic, acce…
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…
A new class of LRS Bianchi type ${\rm VI}_{0}$ cosmological models with free gravitational fields and a variable cosmological term is investigated in presence of perfect fluid as well as bulk viscous fluid. To get the deterministic solution we have imposed the two different conditions over the free gravitational fields. In first case we consider the free gravitational field as magnetic type whereas in second case `gravitational wrench' of unit `pitch" is supposed to be present in free gravitational field. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass…
In this paper, we examine the (LRS) Bianchi-type-I cosmological model with holographic dark energy. The exact solutions to the corresponding field equations are obtained by using generalized hybrid expansion law (HEL). The EoS parameter $ω$ for DE is found to be time dependent and redshift dependent and its exiting range for derived model is agreeing well with the current observations. Here we likewise apply two mathematical diagnostics, the statefinder ({r, s}) and $ω_{d}-ω^{'}_{d}$ plane to segregate HDE model from the $ΛCDM$ model. Here the $ω_{d}-ω^{'}_{d}$ diagnostic trajectories is the g…
In this work we consider particle creation by the expansion of the universe, using two Bianchi type I anisotropic models. The particles studied are of spin 0 and 1/2. The cosmological models have rotational symmetry, which allows us to solve exactly the equations of motion. The number density of the created particles is calculated with the method of Bogolubov transformations.
In this paper, we present a complete classification of Locally Rotationally Symmetric (LRS) Bianchi type I spacetimes according to their Conformal Ricci Collineations (CRCs). When the Ricci tensor is non-degenerate, a general form of the vector field generating CRCs is found, subject to some integrability conditions. Solving the integrability conditions in different cases, it is found that the LRS Bianchi type I spacetimes admit 7, 10, 11 or 15- dimensional Lie algebra of CRCs for the choice of non-degenerate Ricci tensor. Moreover, it is found that these spacetimes admit infinite number of CR…
We study the asymptotic dynamics of $f(T, B)$-theory in an anisotropic Bianchi III background geometry. We show that an attractor always exists for the field equations, which depends on a free parameter provided by the specific $f(T, B)$ functional form. The attractor is an accelerated spatially flat FLRW or non-accelerated LRS Bianchi III geometry. Consequently, the $f(T, B)$-theory provides a spatially flat and isotropic accelerated Universe.
The present study deals with spatially homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with dominance of dark energy. To get the deterministic model of Universe, we assume that the shear scalar $(σ)$ in the model is proportional to expansion scalar $(θ)$. This condition leads to $A=B^{n}$, where $A$,\;$B$ are metric potential and $n$ is positive constant. It has been found that the anisotropic distribution of dark energy leads to the present accelerated expansion of Universe. The physical behavior of the Universe has been discussed in detail.
A model of a cloud formed by massive strings is used as a source of LRS Bianchi type II with time decaying vacuum energy density $Λ$. To construct string cosmological models we have used the energy-momentum tensor for such string as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings, (i) Massive string and (ii) Nambu string. The expansion $θ$ in the model is assumed to be proportional to the shear $σ$. This condition leads to $A=βB^{m}$, where $A$ and $B$ are the metric coefficients, $m$ is a constant and $β$ is an integrating constant. …
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…
Locally-rotationally-symmetric Bianchi type-I viscous and non -viscous cosmological models are explored in general relativity (GR) and in f(R,T) gravity. Solutions are obtained by assuming that the expansion scalar is proportional to the shear scalar which yields a constant value for the deceleration parameter (q=2). Constraints are obtained by requiring the physical viability of the solutions. A comparison is made between the viscous and non-viscous models, and between the models in GR and in f(R,T) gravity. The metric potentials remain the same in GR and in f(R,T) gravity. Consequently, the …
In the present work we revisit the axisymmetric Bianchi VIII and IX models. At the classical level we reproduce the known analytic solution, in a novel way making use of two quadratic integrals of motion, the constraint equation, as well as a linear non-local integral of motion. These quantities correspond to two second rank Killing tensors and a homothetic vector field existing on the relevant configuration space. On the corresponding phase space the two quadratic charges commute with the Hamiltonian constraint but not among themselves. Thus, after turning these charges into operators we obta…
The present study deals with locally rotationally symmetric (LRS) Bianchi type II cosmological models 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 expansion ($θ$) in the models is proportional to the shear ($σ$). This condition leads to $A = B^{m}$, where A and B are the metric coefficients and m is constant. We have derived two types of models depending on different values of m i.e. for $m\neq \sqrt{2}$ and $m = \sqrt{2}$ respectively. For suitable c…
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 propose two higher order generalized uncertainty principles(GUPs) which predict a minimum uncertainty in momentum and apply the deformations that they entail of the Heisenberg algebra to one half of the phase space of the LRS Bianchi I models. After numerically solving the resultant Wheeler Dewitt equations we analyze our solutions and provide evidence that potential IR effects of quantum gravity could have played a role in selecting an overwhelmingly likely geometrical configuration that a quantum universe can possess. In addition we propose a GUP which predicts both a minimum uncertainty …
Following up on hints of anisotropy in the cosmic microwave background radiation (CMB) data, we investigate locally rotational symmetric (LRS) Bianchi type I spacetimes with non-minimally coupled scalar fields. To single out potentially more interesting solutions, we search for Noether symmetry in this system. We then specialize to the Brans-Dicke (BD) field in such a way that the Lagrangian becomes degenerate (nontrivial) and solve the equations for Noether symmetry and the potential that allows it. Then we find the exact solutions of the equations of motion in terms of three parameters and a…
Within the framework of Bianchi type-II (BII) cosmological model the behavior of matter distribution has been considered. It is shown that the non-zero off-diagonal component of Einstein tensor implies some severe restriction on the choice of matter distribution. In particular for a locally rotationally symmetric Bianchi type-II (LRS BII) space-time it is proved that the matter distribution should be strictly isotropic if the corresponding matter field possesses only non-zero diagonal components of the energy-momentum tensor.
We consider the case of $R^n$-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit {\it local rotational symmetry} (LRS). We find exact solutions and study their behaviour and stability in terms of the values of the parameter $n$. In particular, we found a set of cosmic histories in which the universe is initially isotropic, then develops shear anisotropies which approaches a constant value.
In this paper, new exact solutions for locally rotational symmetric (LRS) space-times are obtained within the modified Brans-Dicke theory (MBDT) (Rasouli et al 2014 Class. Quantum Grav. 31 115002). Specifically, extended five-dimensional (5D) versions of Kantowski-Sachs, LRS Bianchi type I and Bianchi type III are investigated in the context of the standard Brans-Dicke theory. We subsequently extract their corresponding dynamics on a 4D hypersurface. Our results are discussed regarding others obtained in the standard Brans-Dicke theory, induced-matter theory and general relativity. Moreover, w…
We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor $F_{μν}$; the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor $T_{μν}$, suffice to reduce the general $F_{μν}$ to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingl…
This paper is devoted to check validity of the laws of thermodynamics for LRS Bianchi type I universe model which is filled with combination of dark matter and dark energy. We take two types of dark energy models, i.e., generalized holographic dark energy and generalized Ricci dark energy. It is proved that the first and generalized second law of thermodynamics are valid on the apparent horizon for both the models. Further, we take fixed radius $L$ of the apparent horizon with original holographic or Ricci dark energy. We conclude that the first and generalized second laws of thermodynamics do…
The Noether symmetry approach is useful tool to restrict the arbitrariness in a gravity theory when the equations of motion are underdetermined due to the high number of functions to be determined in the ansatz. We consider two scalar-coupled theories of gravity, one motivated by induced gravity, the other more standard; in Bianchi I, Bianchi III and Kantowski-Sachs cosmological models. For these models, we present a full set of Noether gauge symmetries, which are more general than those obtained by the strict Noether symmetry approach in our recent work. Some exact solutions are derived using…
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 the present work, focusing on one of the most popular problems in modern gravitation theories, we consider generalized Lanndau-Liftshitz energy-momentum relation to calculate energy distribution of the Bianchi-Type VI spacetime in $f(R)$ gravity. Additionally, the results are specified by using some well-known $f(R)$-gravity models.
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for Locally Rotationally Symmetric (LRS) Bianchi III metric and open Friedmann-Lemaître-Robertson-Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic in…
The work is devoted to LRS Bianchi I domain walls cosmological models within the framework of teleparallel gravity using volumetric expansions laws for the depiction model. The physical and kinematical properties are discussed. The statefinder parameters are also analysed along with the jerk parameter and cosmological constraints.
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 …
This paper has been removed by arXiv administrators because it plagiarizes gr-qc/0011087, gr-qc/0205028, gr-qc/0404108, gr-qc/0212018, and gr-qc/0011027.
For certain models, the energy of the universe which includes the energy of both the matter and the gravitational fields is obtained by using the quasilocal energy-momentum in teleparallel gravity. It is shown that in the case of the Bianchi type I and II universes, not only the total energy but also the quasilocal energy-momentum for any region vanishes independently of the three dimensionless coupling constants of teleparallel gravity.
In the present paper we discuss dynamic of anisotropic Bianchi I Universe filled by the perfect fluid in teleparallel $f(T)$-gravity. By using as analytical as numerical approaches we confirm the main results of previous authors such as presence of future isotropic attractor and find a number of the new one such as existence of essential number of bounce solutions and possibility to construct late time acceleration without any specific matter.
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.
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.
We investigate electromagnetic, gravitational, and plasma related perturbations to first order on homogeneous and hypersurface orthogonal locally rotationally symmetric (LRS) class II spacetimes. Due to the anisotropic nature of the studied backgrounds, we are able to include a non-zero magnetic field to zeroth order. As a result of this inclusion, we find interesting interactions between the electromagnetic and gravitational variables already to first order in the perturbations. The equations governing these perturbations are found by using the Ricci identities, the Bianchi identities, Einste…
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.
This paper is devoted to find the Locally Rotationally Symmetric (LRS) vacuum solutions in the context of f(R) theory of gravity. Actually, we have considered the three metrics representing the whole family of LRS spacetimes and solved the field equations by using metric approach as well as the assumption of constant scalar curvature. It is mention here that R may be zero or non-zero. In all we found 10 different solutions.
The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. In this context, we study the exact vacuum solutions of Bianchi type I, III and Kantowski-Sachs spacetimes in the metric version of f(R) gravity. The field equations are solved by taking expansion scalar theta proportional to shear scalar sigma which gives A=B^n, where A and B are the metric coefficients. The physical behavior of the solutions has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated in each case.
In the continuum the Bianchi identity implies a relationship between different components of the curvature tensor, thus ensuring the internal consistency of the gravitational field equations. In this paper an exact form for the Bianchi identity in Regge's discrete formulation of gravity is derived, by considering appropriate products of rotation matrices constructed around null-homotopic paths. It implies an algebraic relationship between deficit angles belonging to neighboring hinges. As in the continuum, the derived identity is valid for arbitrarily curved manifolds, without a restriction to…
Using the instanton representation method we construct a general solution for GR in the spatially homogeneous case restricted to diagonal variables. This paper provides a testing ground and physical intuition for many of the salient features of general relativity which it is suggested should be preserved in the full theory.
