Bianchi Type-Ⅱ Inflationary Models with Stiff Matter and Decaying Cosmological Term

We deal with Einstein＇s field equations with a time-decaying cosmological term of the forms （i） ∧=β（a/a） ＋ α/a62 and （ii）∧ = α/a^2, where a is the average scale factor of the universe, α and β are constants for a spatially homogeneous and anisotropic LRS Bianchi type-Ⅱ spacetime. Exact solutions of the field equations for stiff matter are obtained by applying a special law of variation for the Hubble parameter. Anisotropic cosmological models are presented with a constant negative deceleration parameter which corresponds to the accelerated phase of the present universe. The cosmological constant A is obtained as a decreasing function of time that is approaching a small positive value at the present epoch, which is corroborated by the consequences from recent supernovae Ia observations. The physical and kinematical behaviors of the models are also discussed.     

Higher-Dimensional Cosmological Models with Density-Parameter-Dependent Cosmological Constant

We discuss the evolution of the scale factor in a higher-dimensional cosmological model in which the cosmological constant is given by the scalar arisen by the contraction of the stress-energy tensor.     

Anisotropic Bianchi Type Ⅰ Cosmological Models with Generalized Chaplygin Gas and Dynamical Gravitational and Cosmological Constants

This paper deals with study of generalized Chaplygin gas model with dynamical gravitational and cosmological constants. In this paper a new set of exact solutions of Einstein field equations for spatially homogeneous and anisotropic Bianchi type Ⅰ space-time have been obtained. The solutions of the Einstein's field equations are obtained by considering(i) the power law relation between Hubble parameter H and scale factor R and(ii) scale factor of the form R =-1/t + t~2, t 1. The assumptions lead to constant and variable deceleration parameter respectively. The physical and dynamical behaviors of the models have been discussed with the help of graphical representations. Also we have discussed the stability and physical acceptability of solutions for solution type-Ⅰ and solution type-Ⅱ.     

Five-Dimensional Cosmological Model with Variable G and A

Einstein＇s field equations with C and A both varying with time are considered in the presence of a perfect fluid for five-dimensional cosmological model in a way which conserves the energy momentum tensor of the matter content. Several sets of explicit solutions in the five-dimensional Kaluza-Klein type cosmological models with variable G and A are obtained. The diminishment of extra dimension with the evolution of the universe for the five-dimensional model is exhibited. The physical properties of the models are examined.     

Exact Solution in Chaotic Inflation Model with Potential Minima

Taking the cosmological expansion rate directly as a function of field , H = H( ), we present a new exact solution to Einstein‘s equations that describe the evolution of cosmological chaotic inflation model. The inflation is driven by the evolution of scalar field with inflation potential V( ) = λ 2 v2)2.8 ( 2- 2)2.The spectral indices of the scalar density ns and gravitational wave fluctuations ng are computed. The value of ns lies well inside the limits set by the cosmic background explorer satellite.     

A Solvable Model in Two—Dimensional Gravity Coupled to a Nonlinear Matter Field

The two-dimensional gravity model with a coupling constant k=4 and a vanishing cosmological constant coupled to a nonlinear matter field is investigated.We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically.These soulutions may be used to describe the naked singularity at the origin.     

Cosmological applications in Kaluza-Klein theory

The field equations of Kaluza–Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor’s expansion of cosmological function, Λ(t), up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed.     

Bianchi Type-Ⅲ String Cosmological Model With Bulk Viscosity and Magnetic Field

The Bianchi type-Ⅲ cosmological model for a cloud string in the presence of bulk viscosity and magnetic field are presented. To obtain the determinate model it is assumed that there is an equation of state ρ = kA and the scalar of expansion is proportional to the shear scalar θ ∝ σ, which leads to a relation between metric potentials B = mC^n. The physical and geometric aspects of the model are also discussed. The model describes a shearing non-rotating continuously expanding universe with a big-bang start. In the absence of magnetic field, it reduces to the string model with bulk viscosity that was previously given in the literature.     

On certain new exact solutions of the Einstein equations for axisymmetric rotating fields

We investigate the Einstein field equations corresponding to the Weyl-Lewis-Papapetrou form for an axisymmetric rotating field by using the classical symmetry method. Using the invafiance group properties of the governing system of partial differential equations （PDEs） and admitting a Lie group of point transformations with commuting infinitesimal generators, we obtain exact solutions to the system of PDEs describing the Einstein field equations. Some appropriate canonical variables are characterized that transform the equations at hand to an equivalent system of ordinary differential equations and some physically important analytic solutions of field equations are constructed. Also, the class of axially symmetric solutions of Einstein field equations including the Papapetrou solution as a particular case has been found.     

A Modified Gravity Theory: Null Aether

General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories with preferred direction established at every point of spacetime by a fixed-norm vector field. The dynamical vector field defined in this way is referred to as the "aether". In this paper, we put forward the idea of a null aether field and introduce, for the first time, the Null Aether Theory(NAT) — a vector-tensor theory. We first study the Newtonian limit of this theory and then construct exact spherically symmetric black hole solutions in the theory in four dimensions, which contain Vaidya-type non-static solutions and static Schwarzschild-(A)dS type solutions, Reissner-Nordstr?m-(A)dS type solutions and solutions of conformal gravity as special cases. Afterwards, we study the cosmological solutions in NAT:We find some exact solutions with perfect fluid distribution for spatially flat FLRW metric and null aether propagating along the x direction. We observe that there are solutions in which the universe has big-bang singularity and null field diminishes asymptotically. We also study exact gravitational wave solutions — AdS-plane waves and pp-waves — in this theory in any dimension D ≥ 3. Assuming the Kerr-Schild-Kundt class of metrics for such solutions, we show that the full field equations of the theory are reduced to two, in general coupled, differential equations when the background metric assumes the maximally symmetric form. The main conclusion of these computations is that the spin-0 aether field acquires a "mass" determined by the cosmological constant of the background spacetime and the Lagrange multiplier given in the theory.     

Static Axially Symmetric Models and Structure Scalars in Self-Interacting Brans–Dicke Gravity

This paper investigates static axially symmetric models in self-interacting Brans–Dicke gravity. We discuss physically feasible sources of models, derive field equations as well as evolution equations from Bianchi identities and construct structure scalars. Using these scalars and evolution equations, the inhomogeneity factors of the system are evaluated. It is found that structure scalars related to double dual of Riemann tensor control the density inhomogeneity.Finally, we obtain exact solutions of homogenous isotropic and inhomogeneous anisotropic spheroid models. It turns out that homogenous solutions reduce to Schwarzschild type interior solutions for a spherical case. We conclude that homogenous models involve homogenous distribution of scalar field whereas inhomogeneous correspond to inhomogeneous scalar field.     

Cosmological applications in Kaluzaben Klein theory

The field equations of Kaluza-Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor's expansion of cosmological function, Λ(t), up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed.     

Spatially Homogeneous Bianchi Type V Cosmological Model in the Scale-Covariant Theory of Gravitation

We discuss spatially homogeneous and anisotropic Bianchi type-V spacetime filled with a perfect fluid in the framework of the seale-covariant theory of gravitation proposed by Canuto et al. By applying the law of variation for Hubble＇s parameter, exact solutions of the field equations are obtained, which correspond to the model of the universe having a big-bang type singularity at the initial time t = 0. The cosmological model, evolving from the initial singularity, expands with power-law expansion and gives essentially an empty space for a large time. The physical and dynamical properties of the model are also discussed.     

A three-dimensional time-dependent theory for helix traveling wave tubes in beam-wave interaction

This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beamwave interaction.The radio frequency electromagnetic fields are represented as the superposition of azimuthally symmetric waves in a vacuum sheath helix.Coupling impedance is introduced to the electromagnetic field equations’ stimulating sources,which makes the theory easier and more flexible to realize.The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations.The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included.The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields,focusing fields and space-charge fields.The numerically simulated results of a tube are presented.     

Some Magnetized Bulk Viscous String Cosmological Models in Cylindrically Symmetric Inhomogeneous Universe with Variable ∧-Term

Some cylindrically symmetric inhomogeneous viscous fluid string cosmological models with magnetic field and cosmological term A varying with time are investigated. To get the deterministic solution, it has been assumed that the expansion （θ） in the model is proportional to the eigen value σ^11 of the shear tensor σ^ij. The value of cosmological constant for the model is found to be small and positive, which is supported by the results from recent supernovae Ia observations. The effect of bulk viscosity is to produce a change in perfect fluid and hence exhibits essential influence on the character of the solution. The physical and geometric properties of the models are also discussed in presence and absence of magnetic field.     

Novel Rotating Hairy Black Hole in （2 ＋ 1） Dimensions

We present some novel rotating hairy black hole metric in （2 ＋ 1） dimensions, which is an exact solution to the field equations of the Einstein-scalar-AdS theory with a non-minimal coupling. The scalar potential is determined by the metric ansatz and consistency of the field equations and cannot be prescribed arbitrarily. In the simplified, critical ease, the scalar potential contains two independent constant parameters, which are respectively related to the mass and angular momentum of the black hole in a particular way. As long as the angular momentum does not vanish, the metric can have zero, one or two horizons. The case with no horizon is physically uninteresting because of the curvature singularity lying at the origin. We identify the necessary conditions for at least one horizon to be present in the solution, which imposes some bound on the mass-angular momentum ratio. For some particular choice of pararneters our solution degenerates into some previously known black hole solutions.     

Exact Solutions to a Combined sinh-cosh-Gordon Equation

Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations （PDEs） with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient the resulting equations by some methods. As an application, are formally derived. ordinary differential equations, then we seek for solutions to exact solutions for the combined sinh-cosh-Gordon equation     

Improved Speed and Shape of Ion-Acoustic Waves in a Warm Plasma

The basic set of fluid equations can be reduced to the nonlinear Kortewege-de Vries(KdV)and nonlinear Schro¨dinger(NLS)equations.The rational solutions for the two equations has been obtained.The exact amplitude of the nonlinear ion-acoustic solitary wave can be obtained directly without resorting to any successive approximation techniques by a direct analysis of the given field equations.The Sagdeev’s potential is obtained in terms of ion acoustic velocity by simply solving an algebraic equation.The soliton and double layer solutions are obtained as a small amplitude approximation.A comparison between the exact soliton solution and that obtained from the reductive perturbation theory are also discussed.     

Variable Separation and Exact Solutions to Generalized Nonlinear Diffusion Equations

We study in detail a method to find the generalized nonlinear diffusion equations,which can be solved by means of the variable separation approach.A complete list of canonical forms for such equations,which admit the functional separable solutions,is botained and some exact solutions to the resulting equations are described. A number of methods have been proven to be effective for finding symmetry reductions and constructing exact solutions to nonlinear diffusion equations.     

Cosmological Constant or Variable Dark Energy？

Selection statics of the Akaike information criterion （AIC） model and the Bayesian information criterion （BIC） model are applied to the A-cold dark matter （ACDM） cosmological model, the constant equation of state of dark energy, w =constant, and the parametrized equation of state of dark energy, w（z） = wo ＋ wlz/（1 ＋ z）, to determine which one is the better cosmological model to describe the evolution of the universe by combining the recent cosmic observational data including She Ia, the size of baryonic acoustic oscillation （BAO） peak from SDSS, the three-year WMAP CMB shift parameter. The results show that AIC, BIC and current datasets are not powerful enough to discriminate one model from the others, though odds suggest differences between them.