Perfect fluid bianchi Type-I cosmological models with time varying <Emphasis Type="Italic">G</Emphasis> and Λ

Bianchi Type-I cosmological models containing perfect fluid with time varying G and Λ have been presented. The solutions obtained represent an expansion scalar θ bearing a constant ratio to the anisotropy in the direction of space-like unit vector λ ⁱ . Of the two models obtained, one has negative vacuum energy density, which decays numerically. In this model, we obtain Λ ∼ H ², Λ ∼ R ₄₄/R and Λ ∼ T ⁻² (T is the cosmic time) which is in accordance with the main dynamical laws for the decay of Λ. The second model reduces to a static solution with repulsive gravity.      

Exact solutions of Einstein and Einstein-scalar equations in 2 + 1 dimensions

A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant Λ and null fluid) in 2 + 1 dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For Λ = 0, the spacetime is though not flat, the Kretschmann invariant vanishes. The energy, momentum, and power output for this metric are obtained. Further a static and circularly symmetric exact solution of the Einsteinmassless scalar equations is given, which has a curvature singularity atr = 0 and the scalar field diverges atr = 0 as well as at infinity.     

A class of new LRS Bianchi type-I perfect fluid universes with decaying vacuum energy density Λ

A class of new LRS Bianchi type-I cosmological models with a variable cosmological term is investigated in presence of perfect fluid. A procedure to generate new exact solutions to Einstein’s field equations is applied to LRS Bianchi type-I space-time. Starting from some known solutions a class of new perfect fluid solutions of LRS Bianchi type-I are obtained. The cosmological constant Λ is found to be positive and a decreasing function of time which is supported by results from recent supernovae Ia observations. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.     

Bulk Viscous Bianchi-III Models with Time Dependent G and?Λ

Bulk Viscous anisotropic Bianchi-III cosmological models are investigated with time dependent gravitational and cosmological constants in the framework of Einstein’s general relativity. In order to get some useful information about the time varying nature of G and Λ, we have assumed an exponentially decaying rest energy density of the universe. The extracted Newtonian gravitational constant G varies with time but its time varying nature depends on bulk viscosity and the anisotropic nature of the model. The cosmological constant Λ is found to decrease with time to a small but positive value for the models.     

Anisotropic Universe Models with Perfect Fluid and Dark Energy with Time Varying G and Λ

We have investigated general Bianchi type I cosmological models which containing a perfect fluid and dark energy with time varying G and Λ that have been presented. The perfect fluid is taken to be one obeying the equation of state parameter, i.e., p=ωρ; whereas the dark energy density is considered to be either modified polytropic or the Chaplygin gas. Cosmological models admitting both power-law which is explored in the presence of perfect fluid and dark energy too. We reconstruct gravitational parameter G, cosmological term Λ, critical density ρ _c , density parameter Ω, cosmological constant density parameter Ω _Λ and deceleration parameter q for different equation of state. The present study will examine non-linear EOS with a general nonlinear term in the energy density.     

Generalized self-similar scalar-tensor theories

In order to analyze how the gravitational constant, G, and the cosmological constant, Λ, may vary we study through symmetry principles the form of the functions in the generalized scalar-tensor theories under the self-similar hypothesis. The results obtained are absolutely general and valid for all the Bianchi models and the flat FRW one. We study the concrete example of the Kantowski–Sachs model finding some new exact self-similar solutions.     

Bianchi Type V Universe Models with Specific Expansion Anisotropy

We investigate Bianchi type V cosmological models for perfect fluid source with time varying cosmological term Λ. We examine the possibility of cosmological models assuming the expansion anisotropy (the ratio σ/θ of the shear scalar σ to the volume expansion θ) to be a function of average scale factor R. The resulting models begin with initial anisotropy and approach isotropy at late times. Our models present an initial epoch with decelerating expansion followed by late time acceleration consistent with observations.     

Classification of the FRW universe with a cosmological constant and a perfect fluid of the equation of state <Emphasis Type="Italic">p</Emphasis> = <Emphasis Type="Italic">w</Emphasis><Emphasis Type="Italic">ρ</Emphasis>

We systematically study the evolution of the Friedmann–Robertson–Walker (FRW) universe coupled with a cosmological constant Λ and a perfect fluid that has the equation of state p = w ρ, where p and ρ denote, respectively, the pressure and energy density of the fluid, and w is an arbitrary real constant. Depending on the specific values of w, Λ, and the curvature k of 3-dimensional space, we separate all of the solutions into various cases. In each case the main properties of the evolution are given in detail, including the periods of deceleration and/or acceleration, and the existence of big bang, big crunch, and big rip singularities. In some cases, errors in classification and interpretation appearing in standard textbooks have been corrected.     

Bianchi Type-III Bulk Viscous and Barotropic Perfect Fluid Cosmological Models in Lyra’s Geometry

We have investigated Bianchi type III bulk viscous and barotropic perfect fluid cosmological models in the frame work of Lyra’s geometry. To get deterministic models of universe, we have assumed the three conditions: (i) shear scalar (σ) is proportional to the expansion (θ). This leads to B=C ⁿ , where B and C are metric potentials. (ii) In presence of viscous fluid, the coefficient of viscosity of dissipative fluid is a power function of mass density ξ=ξ ₀ ρ ^m , where ξ ₀ and m are constant and (iii) in absence of viscosity, a proportionality relation between pressure and energy density of barotropic perfect fluid p=αρ, where α is a proportionality constant. In all the cases, we observed that the displacement vector β is large at beginning of the universe and reduces fast during its evolution so that its nature coincide with the behavior of cosmological constant Λ.     

Some Exact Bianchi Type-V Perfect Fluid Cosmological Models with Heat Flow and Decaying Vacuum Energy Density Λ: Expressions for Some Observable Quantities

In this paper we have obtained some new exact solutions of Einstein’s field equations in a spatially homogeneous and anisotropic Bianchi type-V space-time with perfect fluid distribution along with heat-conduction and decaying vacuum energy density Λ by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. We find that the constant value of deceleration parameter is reasonable for the present day universe. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein’s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The cosmological constant Λ is found to be a decreasing function of time and positive which is corroborated by results from recent supernovae Ia observations. Expressions for look-back time-redshift, neoclassical tests (proper distance d(z)), luminosity distance red-shift and event horizon are derived and their significance are described in detail. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.     

Higher Dimensional FRW Cosmology with Variable G and Λ

We have considered higher dimensional cosmological models of the FRW model with variable G and Λ. The solutions have been obtained for flat model with particular form of cosmological constant. The cosmological parameters have also been obtained for dust, radiation and stiff matter. Physical parameters of the models are discussed.     

Fundamental constants in singularity-free five-dimensional Kaluza-Klein cosmological model

Expressions for the time dependence of the fundamental constants are derived through dimensional reduction and one-loop quantum corrections to scalar fields. Moreover, singularity-free solutions of Einstein's field equations are obtained. Using these solutions, we discuss the time dependence of fundamental constants. It is interesting to see that the fine structure constant asymptotically approaches to 1/137,G _eff (effective four-dimensional constant) approachesG _N (Newtonian gravitational constant), and _eff vanishes. Graphical representations of these results are also given for a special case.     

Cosmological Implications of Interacting Polytropic Gas Dark Energy Model in Non-flat Universe

The polytropic gas model is investigated as an interacting dark energy scenario. The cosmological implications of the model including the evolution of EoS parameter w _Λ, energy density Ω_Λ and deceleration parameter q are investigated. We show that, depending on the parameter of model, the interacting polytropic gas can behave as a quintessence or phantom dark energy. In this model, the phantom divide is crossed from below to up. The evolution of q in the context of polytropic gas dark energy model represents the decelerated phase at the early time and accelerated phase later. The singularity of this model is also discussed. Eventually, we establish the correspondence between interacting polytropic gas model with tachyon, K-essence and dilaton scalar fields. The potential and the dynamics of these scalar field models are reconstructed according to the evolution of interacting polytropic gas.     

Critical Points Inside the Gaps of Ground State Laminations for Some Models in Statistical Mechanics

We consider models of interacting particles situated in the points of a discrete set Λ. The state of each particle is determined by a real variable. The particles are interacting with each other and we are interested in ground states and other critical points of the energy (metastable states). Under the assumption that the set Λ and the interaction are symmetric under the action of a group G—which satisfies some mild assumptions—, that the interaction is ferromagnetic, as well as periodic under addition of integers, and that it decays with the distance fast enough, it was shown in a previous paper that there are many ground states that satisfy an order property called self-conforming or Birkhoff. Under some slightly stronger assumptions all ground states satisfy this order property. Under the assumption that the interaction decays fast enough with the distance, we show that either the ground states form a one dimensional family or that there are other Birkhoff critical points which are not ground states, but lying inside the gaps left by ground states. This alternative happens if and only if a Peierls–Nabarro barrier vanishes. The main tool we use is a renormalized energy. In the particular case that the set Λ is a one dimensional lattice and that the interaction is just nearest neighbor, our result establishes Mather’s criterion for the existence of invariant circles in twist mappings in terms of the vanishing of the Peierls–Nabarro barrier. The work of RdlL was supported by NSF grants. The work of EV was supported by GNAMPA and MIUR Variational Methods and Nonlinear Differential Equations.     

A New Class of Inhomogeneous Cosmological Models with Electromagnetic Field in Normal Gauge for Lyra’s Manifold

A new class of exact solutions of Einstein’s modified field equations in inhomogeneous space-time for perfect fluid distribution with electromagnetic field is obtained in the context of normal gauge for Lyra’s manifold. We have obtained solutions by considering the time dependent displacement field. The source of the magnetic field is due to an electric current produced along the z-axis. Only F ₁₂ is a non-vanishing component of the electromagnetic field tensor. It has been found that the displacement vector β(t) behaves like the cosmological constant Λ in the normal gauge treatment and the solutions are consistent with the recent observations of Type Ia supernovae. Physical and geometric aspects of the models are also discussed in the presence of magnetic field.     

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on Ġ may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.      

Neutral perfect fluids of Majumdar-type in general relativity

We consider the extension of the Majumdar-type class of static solutions for the Einstein-Maxwell equations proposed by Ida to include charged perfect fluid sources. We impose the equation of state ρ+3p = 0 and discuss spherically symmetric solutions for the linear potential equation satisfied by the metric. In this particular case the fluid charge density vanishes and we locate the arising neutral perfect fluid in the intermediate region defined by two thin shells with respective charges Q and −Q. With its innermost flat and external (Schwarzschild) asymptotically flat spacetime regions, the resultant condenser-like geometries resemble solutions discussed by Cohen and Cohen in a different context. We explore this relationship and point out an exotic gravitational property of our neutral perfect fluid. We mention possible continuations of this study to embrace non-spherically symmetric situations and higher dimensional spacetimes.     

Bianchi Type III Cosmological Models for Barotropic Perfect Fluid Distribution with Variable <Emphasis Type="Italic">G</Emphasis> and <Emphasis Type="BoldItalic">Λ</Emphasis>

Bianchi type III cosmological model for perfect fluid distribution with variable G and Λ are investigated. To get the determinate models, we have assumed the barotropic condition p=γ ρ and shear (σ) is proportional to expansion (θ) where p is isotropic pressure, ρ the matter density and 0≤γ≤1. The physical and geometrical aspects related with the observations and singularities in the models are discussed.     

Cylindrically symmetric Zel'dovich fluid distributions in general theory of relativity

The problem of charged perfect fluid distribution is investigated when the space-time is described by the Einstein-Rosen metric. It is shown that with assumed cylindrical symmetry the cosmological constant vanishes, the electromagnetic field becomes source-free, and the perfect fluid reduces to Zel'dovich fluid withp=. Sets of exact solutions for this case have been obtained and the corresponding solutions for Brans-Dicke-Maxwell fields have been derived. For these solutions the Einstein-Rosen metric, however, goes over to three-parameter Marder metric in Brans-Dicke theory.