Two-Fluid Dark Energy Models in Bianchi Type-III Universe with Variable Deceleration Parameter

Some new exact solutions of Einstein’s field equations have come forth within the scope of a spatially homogeneous and anisotropic Bianchi type-III space-time filled with barotropic fluid and dark energy by considering a variable deceleration parameter. We consider the case when the dark energy is minimally coupled to the perfect fluid as well as direct interaction with it. Under the suitable condition, the anisotropic models approach to isotropic scenario. We also find that during the evolution of the universe, the equation of state (EoS) for dark energy ω ^(de), in both cases, tends to ?1 (cosmological constant, ω ^(de)=?1), by displaying various patterns as time increases, which is consistent with recent observations. The cosmic jerk parameter in our derived models are in good agreement with the recent data of astrophysical observations under appropriate condition. It is observed that the universe starts from an asymptotic Einstein static era and reaches to the ΛCDM model. So from recently developed Statefinder parameters, the behaviour of different stages of the universe has been studied. The physical and geometric properties of cosmological models are also discussed.     

Holographic Dark Energy (DE) Cosmological Models with Quintessence in Bianchi Type-V Space Time

In this paper, author studied homogeneous and anisotropic Bianchi type-V universe filled with matter and holographic dark energy (DE) components. The exact solutions to the corresponding Einstein’s field equations are obtained for exponential and power-law volumetric expansion. The holographic dark energy (DE) EoS parameter behaves like constant, i.e. ω _Λ =?1, which is mathematically equivalent to cosmological constant (Λ) for exponential expansion of the model, whereas the holographic dark energy (DE) EoS parameter behaves like quintessence for power-law expansion of the model. A correspondence between the holographic dark energy (DE) models with the quintessence dark energy (DE) is also established. Quintessence potential and dynamics of the quintessence scalar field are reconstructed, which describe accelerated expansion of the universe. The statefinder diagnostic pair {r,s} is adopted to characterize different phases of the universe.     

Interacting Generalized Ghost Dark Energy in Non-isotropic Background

In this work, the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity is investigated. At first, the non-interacting generalized ghost dark energy in a Bianchi type I (BI) background is discussed. Then the equation of state parameter, ω _D = p _D /ρ _D , the deceleration parameter, and the evolution equation of the generalized ghost dark energy are obtained. It was found that, in this case, ω _D cannot cross the phantom line (ω _D >?1) and eventually the universe approaches a de-Sitter phase of expansion (ω _D →?1). Then, this investigation was extended to the interacting ghost dark energy in a non-isotropic universe. It was found that the equation of state parameter of the interacting generalized ghost dark energy can cross the phantom line (ω _D <?1) provided the parameters of the model are chosen suitably. It was considered a specific model which permits the standard continuity equation in this theory. Besides Ω_Λ and Ω _m in standard Einstein cosmology, another density parameter, Ω _σ , is expected by the anisotropy. The anisotropy of the universe decreases and the universe transits to an isotropic flat FRW universe accommodating the present acceleration.     

Instability of Interacting Ghost Dark Energy Model in an Anisotropic Universe

A new dark energy model called “ghost dark energy” was recently suggested to explain the observed accelerating expansion of the universe. This model originates from the Veneziano ghost of QCD. The dark energy density is proportional to Hubble parameter, ρ _Λ = α H, where α is a constant of order \({\Lambda }^{3}_{QCD}\) and Λ _{Q C D} ～ 100M e V is QCD mass scale. In this paper, we investigate about the stability of generalized QCD ghost dark energy model against perturbations in the anisotropic background. At first, the ghost dark energy model of the universe with spatial BI model with/without the interaction between dark matter and dark energy is discussed. In particular, the equation of state and the deceleration parameters and a differential equation governing the evolution of this dark energy model are obtained. Then, we use the squared sound speed \({v_{s}^{2}}\) the sign of which determines the stability of the model. We explore the stability of this model in the presence/absence of interaction between dark energy and dark matter in both flat and non-isotropic geometry. In conclusion, we find evidence that the ghost dark energy might can not lead to a stable universe favored by observations at the present time in BI universe.     

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.     

Holographic Dark Energy Model with Time Varying G as Well as c 2 Parameter

In this paper, we study a holographic dark energy model with time varying gravitational constant G as well as holographic parameter c ² in flat FRW space-time geometry. We obtain the evolution of equation of state parameter and the exact differential equation, which determine the evolution of the dark energy density based on varying G and c ² parameter. Also, we determine the deceleration parameter to explain the expansion of the universe. Further, we study the validity of the generalized second law of thermodynamics in this scenario. Finally, we find out a cosmological implication of our work by evaluating the holographic dark energy equation of state for low red-shifts containing both varying G and c ² parameter corrections.     

Gravitational Collapse of Dust Cloud with Dark Energy

In this paper, we have investigated the gravitational collapse of a spherically symmetric star with anisotropic pressure, made of a dust fluid and dark energy with equations of state p _t =wρ and p _r =kρ, {(k+2w)<?1}. We have considered three cases. First with dust cloud, the second with dark energy and the third with both dust cloud and dark energy without interaction. The effects of dark energy on the gravitational collapse has been studied. It is found that when only dark energy is present, black hole can never be formed. When both dust cloud and dark energy are present, a black hole is formed. This work provides a generalization of the work by Cai and Wang for isotropic pressure to anisotropic pressure (Cai and Wang in Phys. Rev. D 73:063005, 2006).     

QCD Ghost Dark Energy in RS II Braneworld with Bulk-Brane Interaction

We investigate the QCD ghost model of dark energy in the framework of RS II braneworld. We assume there is an energy flow between the brane and bulk, and hence the continuity equation for the ghost dark energy is violated, while it is still preserved for the dark matter on the brane. We find that with the brane-bulk interaction, the equation of state parameter of ghost dark energy on the brane, can cross the phantom line w _D =?1 at the present time, which confirms by some cosmological evidences. This result is in contrast to the standard cosmology where w _D of ghost dark energy never cross the phantom line and the universe enters a de Sitter phase at the late time.     

Evolution of Dark Energy in the Open Universe

In this paper we discuss the evolution of the dark energy in the open universe under the framework of the χCDM model. It is showed that the dark energy in the open universe, which drives the universe accelerating, had strange evolution behaviors: it was in the state of negative energy and positive pressure at the early stage of evolution of the dark energy, then evolved into the phase of negative energy and negative pressure during the middle period, and evolved to have the typical features of dark energy (positive energy and negative pressure) only at the later stage.     

Bianchi Type-II Dark Energy Model in f(R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi Type-II space-time dark energy model with EoS parameter is considered in the presence of a perfect fluid source in the framework of f(R,T) gravity proposed by Harko et al. (Phys. Rev. D, 84:024020, 2011). With the help of special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B, 74:182, 1983) a dark energy cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=λT. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

A Note on Holographic Dark Energy with Varying <Emphasis Type="Italic">c</Emphasis><Superscript>2</Superscript> Term

We reconsider the holographic dark energy (HDE) model with a slowly time varying c ²(z) parameter in the energy density, namely \(\rho _{D}=3{M_{p}^{2}} c^{2}(z)/L^{2}\), where L is the IR cutoff and z is the redshift parameter. As the system’s IR cutoff we choose the Hubble radius and the Granda-Oliveros (GO) cutoffs. The latter inspired by the Ricci scalar curvature. We derive the evolution of the cosmological parameters such as the equation of state and the deceleration parameters as the explicit functions of the redshift parameter z. Then, we plot the evolutions of these cosmological parameters in terms of the redshift parameter during the history of the universe. Interestingly enough, we observe that by choosing L = H ^?1 as the IR cutoff for the HDE with time varying c ²(z) term, the present acceleration of the universe expansion can be achieved, even in the absence of interaction between dark energy and dark matter. This is in contrast to the usual HDE model with constant c ² term, which leads to a wrong equation of state, namely that for dust w _D =0, when the IR cutoff is chosen the Hubble radius.     

A Modified Generalized Chaplygin Gas as the Unified Dark Matter–Dark Energy Revisited

A modified generalized Chaplygin gas (MGCG) is considered as the unified dark matter–dark energy revisited. The character of MGCG is endued with the dual role, which behaves as matter at early times and as a quiessence dark energy at late times. The equation of state for MGCG is p?=???αρ/(1?+?α)????(z)ρ ^???α /(1?+?α) , where $\vartheta(z)=-[\,\rho_{\,\rm 0c}(1+z)^{3}]\,^{(1+\alpha)}(1-\Omega_{\,\rm 0B})^{\alpha}\{\alpha\Omega_{\,\rm 0DM}+ \Omega_{\,\rm 0DE}[\,\omega_{\,\rm DE}+\alpha(1+\omega_{\rm DE})](1+z)^{3\omega_{\rm DE}(1+\alpha)}\}$ . Some cosmological quantities, such as the densities of different components of the universe Ω _i (i, respectively, denotes baryons, dark matter, and dark energy) and the deceleration parameter q, are obtained. The present deceleration parameter q ₀, the transition redshift z _T, and the redshift z _eq, which describes the epoch when the densities in dark matter and dark energy are equal, are also calculated. To distinguish MGCG from others, we then apply the Statefinder diagnostic. Later on, the parameters (α and ω _DE) of MGCG are constrained by combination of the sound speed $c^{2}_{\rm s}$ , the age of the universe t ₀, the growth factor m, and the bias parameter b. It yields $\alpha=-3.07^{+5.66}_{-4.98}\times10^{-2}$ and $\omega_{\rm DE}=-1.05^{+0.06}_{-0.11}$ . Through the analysis of the growth of density perturbations for MGCG, it is found that the energy will transfer from dark matter to dark energy which reach equal at z _eq～0.48 and the density fluctuations start deviating from the linear behavior at z～0.25 caused by the dominance of dark energy.     

Bianchi Type-III Magnetized Wet Dark Fluid Cosmological Model in General Relativity

Bianchi type-III cosmological model of universe filled with dark energy from a wet dark fluid (WDF) in presence and absence of magnetic field is investigated in general theory of relativity. We assume that F ₁₂ is the only non-vanishing component of F _ij . We obtain exact solutions to the field equations using the condition that expansion is proportional to the shear scalar i.e. (B=C ⁿ ). The physical behavior of the model is discussed with and without magnetic field. We conclude that universe model do not approach isotropy through the evolution of the universe.     

Effects of inhomogeneities on apparent cosmological observables: “fake” evolving dark energy

Using the exact Lemaitre?CBondi?CTolman solution with a non-vanishing cosmological constant ??, we investigate how the presence of a local spherically symmetric inhomogeneity can affect apparent cosmological observables, such as the deceleration parameter or the effective equation of state of dark energy (DE), derived from the luminosity distance under the assumption that the real space-time is exactly homogeneous and isotropic. The presence of a local underdensity is found to produce apparent phantom behavior of DE, while a locally overdense region leads to apparent quintessence behavior. We consider relatively small large scale inhomogeneities which today are not linear and could be seeded by primordial curvature perturbations compatible with CMB bounds. Our study shows how observations in an inhomogeneous ??CDM universe with initial conditions compatible with the inflationary beginning, if interpreted under the wrong assumption of homogeneity, can lead to the wrong conclusion about the presence of ??fake?? evolving dark energy instead of ??.     

Interacting generalized ghost dark energy in a non-flat universe

We investigate the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity. First, we study the non-interacting generalized ghost dark energy in a flat Friedmann-Robertson-Walker (FRW) background. We obtain the equation of state parameter, w _D = p/ρ, the deceleration parameter, and the evolution equation of the generalized ghost dark energy. We find that, in this case, w _D cannot cross the phantom line (w _D > ?1) and eventually the universe approaches a de-Sitter phase of expansion (w _D → ?1). Then, we extend the study to the interacting ghost dark energy in both a flat and non-flat FRW universe. We find that the equation of state parameter of the interacting generalized ghost dark energy can cross the phantom line (w _D < ?1) provided the parameters of the model are chosen suitably. Finally, we constrain the model parameters by using the Markov Chain Monte Carlo (MCMC) method and a combined dataset of SNIa, CMB, BAO and X-ray gas mass fraction.     

Holographic DBI-Essence Dark Energy via Power-Law Solution of the Scale Factor

The present work reports a Holographic reconstruction of Dirac–Born–Infeld (DBI)-essence Dark Energy (DE) in a flat FRW universe. The scale factor a(t) is chosen in power law form. We have reconstructed the scalar field and potential and subsequently the equation of state (EoS) parameter ω of the DBI-essence DE. The corresponding plots show increasing scalar field, decaying tension and decaying potential. The reconstructed EoS parameter stays below ?1, showing a phantom-like behavior. The stability of the reconstructed DBI-essence DE is investigated through squared speed of sound $v_{s}^{2}$ : its negative sign reveals that the holographically reconstructed DBI-essence is classically unstable.     

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.     

Dark energy, cosmic coincidence and future singularity of the universe

Dark energy model with the equation of state $p_{DE} =-\rho _{DE} -A\rho _{DE}^\alpha $ , is characterised by four finite life time future singularity of the universe for different values of the parameter $A$ and $\alpha $ [Nojiri et al. in Phys Rev D 71:063004, 2005]. Since from the matter dominated era to the dark energy dominated era the ratio of the dark energy density to the matter energy density increases as the universe expand for these future singularities, the universe passes through a significant time when the dark energy density and the matter energy density are nearly comparable. Considering $\frac{1}{r_0 }<r=\frac{\rho _{DE} }{\rho _M }<r_0 $ , where $r_0$ is any fixed ratio, we calculate the fraction of total life time of the universe when the universe passes through the coincidental stage for these singularities. It has been found that the fractional time varies as $\alpha $ varies within the range for which these finite life time future singularities occur and the fraction is smaller for smaller values of $r_0 $ . Importance of the fractional time and observational limits onto the values of the parameter $A$ and $\alpha $ has also been discussed.     

Dark energy interacting with dark matter and a third fluid: Possible EoS for this component

A cosmological model of dark energy interacting with dark matter and another general component of the universe is considered. The equations for the coincidence parameters r and s, which represent the ratios between dark energy and dark matter and the other cosmic fluid respectively, are analyzed in terms of the stability of stationary solutions. The obtained general results allow to shed some light on the equations of state of the three interacting fluids, due to the constraints imposed by the stability of the solutions. We found that for an interaction proportional to the sum of the dark energy density and the third fluid density, the hypothetical fluid must have positive pressure, which leads naturally to a cosmological scenario with radiation, unparticle or even some form of warm dark matter as the third interacting fluid.