Anisotropic Bulk Viscous Cosmological Models with?Variable G and Λ

This paper deals with Bianchi-I, Kantowski Sachs and Bianchi-III anisotropic cosmological models of the universe, filled with a bulk viscous cosmic fluid, in the presence of variable gravitational and cosmological constants. A new set of exact solutions of Einstein’s field equation have been obtained in both truncated and full causal theories. Physical behaviour of the models has also been discussed.     

Cosmological analysis of scalar field models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

This paper determines the existence of Noether symmetry in non-minimally coupled f(R, T) gravity admitting minimal coupling with scalar field models. We consider a generalized spacetime which corresponds to different anisotropic and homogeneous universe models. We formulate symmetry generators along with conserved quantities through Noether symmetry technique for direct and indirect curvature–matter coupling. For dust and perfect fluids, we evaluate exact solutions and construct their cosmological analysis through some cosmological parameters. We conclude that decelerated expansion is obtained for the quintessence model with a dust distribution, while a perfect fluid with dominating potential energy over kinetic energy leads to the current cosmic expansion for both phantom as well as quintessence models.     

Bianchi-I Space-time with Variable Gravitational and?Cosmological “Constants”

We consider Einstein’s field equations with variable gravitational and cosmological “constants” for a spatially homogeneous and anisotropic Bianchi-I space-time. A law of variation for the Hubble parameter, which is related to the average scale factor and yields a constant value of the deceleration parameter, is assumed to solve the field equations. The gravitational constant is allowed to follow a power-law form. We find that a time-increasing gravitational constant is suitable for describing the present evolution of universe. The solutions reveal the dynamics of a universe, which expands forever. The physical interpretation of the solutions is discussed in detail.     

Anisotropic dark energy models with constant deceleration parameter

We consider a spatially homogeneous and totally anisotropic Bianchi-I space-time with perfect fluid (dark matter and standard visible matter) and anisotropic dark energy, which has dynamical energy density. The two sources are assumed to interact minimally and therefore their energy momentum tensors are conserved separately. Using suitable physical assumptions, the field equations are solved exactly. Various dark energy models are studied and it is found that quintessence model is suitable for describing the present evolution of the universe. The geometrical and kinematical features of the models and the behavior of the anisotropy of the dark energy, are examined in detail.     

LRS Bianchi type I models with anisotropic dark energy and constant deceleration parameter

Locally rotationally symmetric 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 of Einstein’s field equations are obtained by assuming a special law of variation for the mean Hubble parameter, which yields a constant value of the deceleration parameter. Geometrical and kinematic properties of the models and the behaviour of the anisotropy of the dark energy have been carried out. The models give dynamically anisotropic expansion history for the universe that allows to fine tune the isotropization of the Bianchi metric, hence the CMB anisotropy.     

Chaotic spin precession in anisotropic universes and fermionic dark matter

We consider the precession of a Dirac particle spin in some anisotropic Bianchi universes. This effect is present already in the Bianchi-I universe. In the Bianchi-IX universe it acquires the chaotic character due to the stochasticity of the oscillatory approach to the cosmological singularity. The related helicity flip of fermions in the veryearly Universe may produce the sterile particles contributing to dark matter.     

Isotropic and anisotropic dark energy models

In this review we discuss the evolution of the universe filled with dark energy with or without perfect fluid. In doing so we consider a number of cosmological models, namely Bianchi type I, III, V, VI₀, VI and FRW ones. For the anisotropic cosmological models we have used proportionality condition as an additional constrain. The exact solutions to the field equations in quadrature are found in case of a BVI model. It was found that the proportionality condition used here imposed severe restriction on the energy-momentum tensor, namely it leads to isotropic distribution of matter. Anisotropic BVI₀, BV, BIII and BIDE models with variable EoS parameter ω have been investigated by using a law of variation for the Hubble parameter. In this case the matter distribution remains anisotropic, though depending on the concrete model there appear different restrictions on the components of energy-momentum tensor. That is why we need an extra assumption such as variational a law for the Hubble parameter. It is observed that, at the early stage, the EoS parameter v is positive i.e. the universe was matter dominated at the early stage but at later time, the universe is evolving with negative values, i.e., the present epoch. DE model presents the dynamics of EoS parameter ω whose range is in good agreement with the acceptable range by the recent observations. A spatially homogeneous and anisotropic locally rotationally symmetric Bianchi-I space time filled with perfect fluid and anisotropic DE possessing dynamical energy density is studied. In the derived model, the EoS parameter of DE (ω^(de)) is obtained as time varying and it is evolving with negative sign which may be attributed to the current accelerated expansion of Universe. The distance modulus curve of derived model is in good agreement with SNLS type Ia supernovae for high redshift value which in turn implies that the derived model is physically realistic. A system of two fluids within the scope of a spatially flat and isotropic FRW model is studied. The role of the two fluids, either minimally or directly coupled in the evolution of the dark energy parameter, has been investigated. In doing so we have used three different ansatzs regarding the scale factor that gives rise to a variable decelerating parameter. It is observed that, in the non-interacting case, both the open and flat universes can cross the phantom region whereas in the interacting case only the open universe can cross the phantom region. The stability and acceptability of the obtained solution are also investigated.     

Anisotropy Effects and Observational Data on the Constraints of Evolution Dark Energy Models

We investigate cosmological dark energy models where the accelerated expansion of the universe is driven by a field with an anisotropic universe. The constraints on the parameters are obtained by maximum likelihood analysis using observational of 194 Type Ia supernovae(SNIa) and the most recent joint light-curve analysis(JLA) sample. In particular we reconstruct the dark energy equation of state parameter w(z) and the deceleration parameter q(z). We find that the best fit dynamical w(z) obtained from the 194 SNIa dataset does not cross the phantom divide line w(z) =-1 and remains above and close to w(z)≈-0.92 line for the whole redshift range 0 ≤ z ≤ 1.75 showing no evidence for phantom behavior. By applying the anisotropy effect on the ΛCDM model, the joint analysis indicates that ?_(σ0)= 0.0163 ± 0.03,with 194 SNIa, ?_(σ0)=-0.0032 ± 0.032 with 238 the SiFTO sample of JLA and ?_(σ0)= 0.011 ± 0.0117 with 1048 the SALT2 sample of Pantheon at 1σ′confidence interval. The analysis shows that by considering the anisotropy, it leads to more best fit parameters in all models with JLA SNe datasets. Furthermore, we use two statistical tests such as the usual χ_(min)~2/dof and p-test to compare two dark energy models with ΛCDM model. Finally we show that the presence of anisotropy is confirmed in mentioned models via SNIa dataset.     

Bianchi Type-III Cosmological Models with Anisotropic Dark Energy (DE) in Lyra Geometry

The main purpose of this paper is to explore the solutions of Bianchi type-III cosmological model in Lyra geometry in the background of anisotropic dark energy. The general form of the anisotropy parameter of the expansion for Bianchi type-III space time is obtained in the presence of a single imperfect fluid with a dynamical anisotropic equation of state parameter and a dynamical energy density in Lyra geometry. A special law is assumed for the anisotropy of the fluid with reduces the anisotropy parameter of the expansion to a simple form $\Delta \propto \frac{1}{H^{2}V^{2}}$ . The exact solutions of the field equations, under the assumption on the anisotropy of the fluid, are obtained for exponential and power law volumetric expansion. The isotropy of the fluid, space and expansion are discussed. It is observed that the universe can approach to isotropy monotonically even in the presence of an anisotropic fluid. The anisotropy of the fluid also isotropizes at later times for accelerating models. The expression for the look-back time, proper distance, luminosity distance and angular diameter distance are also derived.     

Phantom Appearance of Non-phantom Matter in Anisotropic Cosmological Model

Two cosmological models with non-phantom matter having the same expansion of the universe as phantom cosmologies are constructed in anisotropic Bianchi type-V universe. The exact solutions to the corresponding Einstein field equations have been obtained. The statefinder diagnostic pair i.e. {r,s} parameters have been obtained for disordered radiation i.e. γ=1/3. We have also discussed the well-known astrophysical phenomena, namely the look-back time, luminosity distance and event horizon with redshift.     

Dynamics of anisotropic power-law <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) cosmology

Modified theories of gravity have attracted much attention of the researchers in the recent years. In particular, the f(R) theory has been investigated extensively due to important f(R) gravity models in cosmological contexts. This paper is devoted to exploring an anisotropic universe in metric f(R) gravity. A locally rotationally symmetric Bianchi type I cosmological model is considered for this purpose. Exact solutions of modified field equations are obtained for a well-known f(R) gravity model. The energy conditions are also discussed for the model under consideration. The viability of the model is investigated via graphical analysis using the present-day values of cosmological parameters. The model satisfies null energy, weak energy, and dominant energy conditions for a particular range of the anisotropy parameter while the strong energy condition is violated, which shows that the anisotropic universe in f(R) gravity supports the crucial issue of accelerated expansion of the universe.     

Unifying phantom inflation with late-time acceleration: scalar phantom–non-phantom transition model and generalized holographic dark energy

The unifying approach to early-time and late-time universe based on phantom cosmology is proposed. We consider gravity-scalar system which contains usual potential and scalar coupling function in front of kinetic term. As a result, the possibility of phantom–non-phantom transition appears in such a way that universe could have effectively phantom equation of state at early time as well as at late time. In fact, the oscillating universe may have several phantom and non-phantom phases. Role in each of two phase and can be absorbed into the redefinition of the scalar field. Right on the transition point, however, the factor cannot be absorbed into the redefinition and play the role to connect two phases smoothly. Holographic dark energy where infrared cutoff is identified with combination of FRW parameters: Hubble constant, particle and future horizons, cosmological constant and universe life-time (if finite). Depending on the specific choice of the model the number of interesting effects occur: the possibility to solve the coincidence problem, crossing of phantom divide and unification of early-time inflationary and late-time accelerating phantom universe. The bound for holographic entropy which decreases in phantom era is also discussed.     

Bianchi type III models with anisotropic dark energy

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 (D μ H^-2V^-2{\Delta\propto H^{-2}V^{-2}}, where Δ is the anisotropy parameter, H is the mean Hubble parameter and V is the volume of the universe). 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, space and expansion are examined. It is observed that the universe can approach to isotropy monotonically even in the presence of an anisotropic fluid. The anisotropy of the fluid also isotropizes at later times for accelerating models and evolves into the well-known cosmological constant in the model for exponential volumetric expansion.     

A Two-Field Dilaton Model of Dark Energy

We investigate the cosmological evolution of a two-field model of dark energy, where one is a dilaton field with canonical kinetic energy and the other is a phantom field with a negative kinetic energy term. Phase-plane analysis shows that the ＂phantom＂-dominated scaling solution is the stable late-time attractor of this type of model. We find that during the evolution of the universe, the equation of state w changes from w 〉 -1 to w 〈 -1, which is consistent with recent observations.     

Bulk Viscous Bianchi Type-III Cosmological Model with Time-Dependent <Emphasis Type="Italic">G</Emphasis> and Λ

This paper deals with Bianchi type-III anisotropic cosmological model of the universe filled with a bulk viscous fluid with time varying gravitational and cosmological constants. It is shown that the field equations are solvable for any arbitrary cosmic scale function. Exact solutions of Einstein’s field equations are obtained which represent an expanding, shearing, non-rotating and decelerating universe. The physical behaviour of the model has also been discussed.     

Bianchi -V Space -Time with Anisotropic Dark Energy in General Relativity

In a spatially homogeneous and anisotropic Bianchi type-V space-time the consequences of the presence of dynamically anisotropic dark energy and perfect fluid with heat-conduction are studied. We assume that dark energy is minimally interacting with matter and has an equation of state which is modified in a consistent way with the conservation of energy momentum tensor. Exact solutions of Einstein field equations are obtained by taking constant value of deceleration parameter. We find that this assumption is reasonable for the observation of the present day universe. The physical and geometrical properties of the models, the behavior of the anisotropy of dark energy and the thermodynamical relations that govern such solutions are discussed in detail.     

Multi-pole dark energy

A scalar field with a pole in its kinetic term is often used to study cosmological inflation; it can also play the role of dark energy, which is called the pole dark energy model. We propose a generalized model where the scalar field may have two or even multiple poles in the kinetic term, and we call it the multi-pole dark energy. We find that the poles can place some restrictions on the values of the original scalar field with a non-canonical kinetic term. After the transformation to the canonical form, we get a flat potential for the transformed scalar field even if the original field has a steep one. The late-time evolution of the universe is obtained explicitly for the two pole model, while dynamical analysis is performed for the multiple pole model. We find that it does have a stable attractor solution, which corresponds to the universe dominated by the potential of the scalar field.     

Living with phantoms fields in a sheet spacetime

We consider the flat anisotropic Bianchi I braneworld model of the universe within the framework of low energy effective string action in four-dimensions including the leading order α′ terms, two-scalar fields, their interaction, non-minimal coupling of the dark-energy scalar field to the scalar curvature and effective cosmological constant. Backward (high energy limit) and forward (low energy limit) in time analytic solutions are derived and late-time accelerated expansion was found. It is shown that during the transition from high energy limit to the low energy limit, the topology of the universe is changing in time: we have a transition from a (1 + 3) FRW homogenous and isotropic spacetime dominated by radiation to a (1 + 2) spacetime sheet dominated by phantom energy while the third spatial dimension is contracted in time. We have also found that dark matter and dark energy may be unified at early epoch in the form of radiation fluids while the late-time dynamics is governed by phantom energy and dark energy. Many interesting features are revealed.     

Self-consistent solutions for cosmological models with rotation

A wide spectrum of new results is obtained describing homogeneous motionless cosmological models with rotation in which causality is not violated. Exact solutions are also given for cosmological models describing an expanding and rotating universe. Sources in the obtained solutions are an anisotropic or ideal fluid, a massless complex scalar field, the electromagnetic field, a radiation field, and various combinations of these sources.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 5–10, June, 1988.     

Bianchi-I Universe with Decaying Vacuum Energy Density and Time Varying Gravitational Constant

Anisotropic Locally Rotationally Symmetric Bianchi-I (LRSBI) 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 Λ are discussed. Our calculations for the Supernova constraints concerning the luminosity distance provide reasonable results.