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.     

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.     

Magnetized anisotropic dark energy models with constant deceleration parameter

In this paper, we have studied the solutions of plane-symmetric Universe with variable ω in the presence and the absence of magnetic field of energy density ρ _B . A special law of variation for Hubble’s parameter proposed by Bermann in Nuovo Cimento B 74, 182 (1983) has been utilized to solve the field equations. Some physical and kinematical properties of the models are also discussed.     

Bianchi type III and Kantowski-Sachs cosmological models in Lyra geometry

Cosmological models for Bianchi type III and Kantowski-Sachs space-times within the framework of Lyra geometry are obtained. The physical behavior of the models is also discussed.     

Magnetized anisotropic cosmological models with varying Λ

Some anisotropic homogeneous cosmological models with electromagnetic field are obtained in presence of a perfect fluid. The source of the magnetic field is due to an electric current produced along the x-axis. Without assuming any ad hoc law, we obtain a cosmological constant as a decreasing function of time which is supported by results from recent supernovae Ia observations. The behaviour of the electromagnetic field tensor together with some physical aspects of the model are also discussed.     

DGP cosmological model with generalized Ricci dark energy

The Higgs-boson decay \(h \rightarrow \gamma \ell ^+ \ell ^-\) for various lepton states \(\ell = (e, \, \mu , \, \tau )\) is analyzed. The differential decay width and forward–backward asymmetry are calculated as functions of the dilepton invariant mass in a model where the Higgs boson interacts with leptons and quarks via a mixture of scalar and pseudoscalar couplings. These couplings are partly constrained from data on the decays to leptons, \(h \rightarrow \ell ^+ \ell ^-\) , and quarks \(h \rightarrow q \bar{q} \) (where \(q = (c, \, b)\) ), while the Higgs couplings to the top quark are chosen from the two-photon and two-gluon decay rates. Nonzero values of the forward–backward asymmetry will manifest effects of new physics in the Higgs sector. The decay width and asymmetry integrated over the dilepton invariant mass are also presented.     

Holographic cosmological constant and dark energy

A general holographic relation between UV and IR cutoff of an effective field theory is proposed. Taking the IR cutoff relevant to the dark energy as the Hubble scale, we find that the cosmological constant is highly suppressed by a numerical factor and the fine tuning problem seems alleviative. We also use different IR cutoffs to study the case in which the universe is composed of matter and dark energy.     

Inhomogeneous dark energy and cosmological acceleration

We study the evolution of an inhomogeneous fluid with self-similarity of the second kind and anisotropic pressure. We found a class of solution to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid is proportional to its energy density () and that the fluid moves along time-like geodesics. The equation of state combined with the self-similarity of second kind implies ω = −1. The energy conditions, geometrical and physical properties of the solutions are studied. We have found that, for the self-similar parameter , the solution represents an accelerated cosmological model ending in a Big Rip stage.     

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.     

Star models with dark energy

We have constructed star models consisting of four parts: (i) a homogeneous inner core with anisotropic pressure (ii) an infinitesimal thin shell separating the core and the envelope; (iii) an envelope of inhomogeneous density and isotropic pressure; (iv) an infinitesimal thin shell matching the envelope boundary and the exterior Schwarzschild spacetime. We have analyzed all the energy conditions for the core, envelope and the two thin shells. We have found that, in order to have static solutions, at least one of the regions must be constituted by dark energy. The results show that there is no physical reason to have a superior limit for the mass of these objects but for the ratio of mass and radius.     

Spherically symmetric anisotropic and inhomogeneous cosmological models

Spherically symmetric cosmological models filled with dust (pressure-free fluid) content are analyzed. It has been pointed out that these models are anisotropic (of non-vanishing shear) and inhomogeneous (∂p/ρr ≠ 0), the characteristics related directly to the presence of the free gravitational field. It is demonstrated that when the free gravitational field vanishes these models degenerate to the corresponding Friedmann-Robertson-Walker (FRW) models. It is further shown that the energy density of the free gravitational field can be introduced into observational cosmology as a new parameter since it enters into the expansion and deceleration equations, as well as conservation law for total energy, implying that the present Hubble velocity can be reached in a shorter time from the big bang. Finally, the effect of shear on the redshift is also discussed. This paper is dedicated to my teacher Professor V V Narlikar on the occasion of his 81st birthday.     

Kantowski-Sachs cosmological model and an inflationary era

We study an empty Kantowski-Sachs universe model with cosmological constant . The characteristic feature of an inflationary era is found. This universe model emerges from a pointlike, stringlike, membranelike singularity and develops toward an isotropic de Sitter universe.     

The Bianki IX cosmological models with a rotating anisotropic liquid

Models of the Universe with the Bianki IX rotation, when the source of gravitation involves accompanying anisotropic liquid, nonaccompanying dustlike liquid, and pure radiation, are suggested. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 77–79, July, 2008.     

Homogeneous anisotropic cosmological models with viscous fluid and magnetic field

The paper presents some exact solutions of Bianchi types I and III and Kantowski-Sachs cosmological models consisting of a dissipative fluid along with an axial magnetic field. A barytropic equation of state (p=), together with a pair of linear relations between the matter density (), the shear scalar (), and the expansion scalar () have been assumed for simplicity. The solutions are basically of two different types, one for the Bianchi I and the other for III and Kantowski-Sachs type. The presence of the magnetic field, however, does not change the fundamental nature of the initial singularity.     

The cosmological constant and dark energy in braneworlds

We review recent attempts to address the cosmological constant problem and the late-time acceleration of the Universe based on braneworld models. In braneworld models, the way in which the vacuum energy gravitates in the 4D spacetime is radically different from conventional 4D physics. It is possible that the vacuum energy on a brane does not curve the 4D spacetime and only affects the geometry of the extra-dimensions, offering a solution to the cosmological constant problem. We review the idea of supersymmetric large extra dimensions that could achieve this and also provide a natural candidate for a quintessence field. We also review the attempts to explain the late-time accelerated expansion of the universe from the large-distance modification of gravity based on the braneworld. We use the Dvali–Gabadadze–Porrati model to demonstrate how one can distinguish this model from dark energy models in 4D general relativity. Theoretical difficulties in this approach are also addressed.     

Gravitational energy in Brans-Dicke cosmological models

The behaviour of gravitational energy and scalar field during the evolution of the universe within the framework of Brans-Dicke theory has been discussed. With help of the Landau-Lifshitz pseudo-tensor for the flat Friedmann-Robertson-Walker model, it is found that (i) the total energy of the universe is always zero, (ii) the Brans-Dicke scalar field for all Ω >-0 contributes energy to the negative energy of gravitational field and this gets transferred to the vacuum energy which accelerates the expansion of the universe.     

Features of holographic dark energy under combined cosmological constraints

We investigate the observational signatures of the holographic dark-energy models, including both the original model and a model with an interaction term between the dark energy and dark matter. We first delineate the dynamical behavior of such models, especially considering whether they would have a “big rip” for different parameters; then we use several recent observations, including 182 high-quality type Ia supernovae data observed with the Hubble Space Telescope, the SNLS and ESSENCE surveys, 42 latest Chandra X-ray cluster gas mass fraction, 27 high-redshift gamma-ray burst samples, the baryon acoustic oscillation measurement from the Sloan Digital Sky Survey, and the CMB shift parameter from the WMAP three-year result to give more reliable and tighter constraints on the holographic dark-energy models. The results of our constraints for the holographic dark-energy model without interaction is c=0.748_−0.009^+0.108, Ω _m0=0.276_−0.016^+0.017, and for the model with interaction (c=0.692_−0.107^+0.135, Ω _m0=0.281_−0.017^+0.017, α=−0.006_−0.024^+0.021, where α is an interacting parameter). As these models have more parameters than the ΛCDM model, we use the Bayesian Evidence as a model-selection criterion to make comparisons. We found that the holographic dark-energy models are mildly favored by the observations as compared to the ΛCDM model.     

爱因斯坦宇宙常数和宇宙中暗能量

综述了宇宙在加速膨胀的观察证据,从爱因斯坦场方程和动力学方程出发详细分析爱因斯坦引入宇宙常数在宇宙加速膨胀中的作用,探讨宇宙常数和宇宙中暗能量的关系．