Anisotropic cosmological models and generalized scalar tensor theory

In this paper generalized scalar tensor theory has been considered in the background of anisotropic cosmological models, namely, axially symmetric Bianchi-I, Bianchi-III and Kortowski-Sachs space-time. For bulk viscous fluid, both exponential and power-law solutions have been studied and some assumptions among the physical parameters and solutions have been discussed.     

Inhomogeneous cosmological models with heat flux

We present a general class of inhomogeneous cosmological models filled with non-thermalized perfect fluid by assuming that the background spacetime admits two space-like commuting Killing vectors and has separable metric coefficients. The singularity structure of these models depends on the choice of the parameters and the metric functions. A number of previously known perfect fluid models follow as particular cases of this general class. Physical and geometrical features of these models are studied and the general expression for temperature distribution is given.     

Conformally invariant scalar field in charge-asymmetric cosmological models

Within a statistical approach to the general theory of relativity, we have constructed isotropic-charge-asymmetric cosmological models with an ultrarelativistic mixture of baryons and antibaryons and a conformally invariant scalar field. We have determined the role of the scalar field in the models obtained. We have investigated the evolution of small perturbations on the background of the spatially flat nonsingular model.Donets Polytechnical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 71–75, January, 1994.     

Causal dissipation in Robertson-Walker cosmological models

Some of the Robertson-Walker cosmological models filled with a fluid with bulk viscosity have been derived which are consistent with causal thermodynamics. The models are discussed briefly.     

Inflationary stages in cosmological models with a scalar field

Homogeneous isotropic cosmological models with a massive scalar field are studied. It is shown that inflationary stages of evolution are characteristic of most solutions in these models.     

Nonsingular cosmological models with torsion determined by vacuum polarization of quantum fields

Nonsingular cosmological models with reducing torsion induced by vacuum quantum effects are constructed. The metric of the models described corresponds to the inflationary universe. Moreover, anisotropic nonsingular cosmological model with constant torsion is constructed.     

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass μ≠0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy–momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g_μ,νρ with ρ>0, thus providing a concrete quantum field theoretic model of the cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p0.     

Cosmological Constant and Stability of the Cosmological Models

The importance of cosmological constant for the cosmological models is given. The variations of the cosmological model for parameters λ and k were discussed respectively. Near λ = 0, the cosmological model is unstable with the change of λ, and near λ = β = 0, the cosmological model is unstable with the change of k. So when we consider the stable cosmological model, we must consider the nonzero cosmological constant.     

Inflation in cosmological models with a non-minimally coupled, massless scalar field

A homogeneous, spatially flat cosmological model induced by a massless scalar field is investigated. The parameter ξ of coupling of the field with the curvature can take any value. It is shown that the range of values of ξ is divided into three regions, ξ<0, 0<ξ<1/6, and ξ>1/6, each of which is characterized by the behavior of the scale factor in it. The points ξ=0 and ξ=1/6 are singular. Stages with exponential and power-law inflation are found in the ranges 0<ξ<1/6 and ξ>1/6. An exponential inflationary stage with acceptable cosmological consequences can occur for small positive ξ. Kazan’ State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 53–57, March, 1997.     

The case for the cosmological constant

I present a short overview of current observational results and theoretical models for a cosmological constant. The main motivation for invoking a small cosmological constant (or A-term) at the present epoch has to do with observations of high redshift Type Ia supernovae which suggest an accelerating universe. A flat accelerating universe is strongly favoured by combining supernovae observations with observations of CMB anisotropies on degree scales which give the ‘best-fit’ values Θ_A ⋍ 0.7 and Θ _m ⋍ 0.3. A time dependent cosmological A-term can be generated by scalar field models with exponential and power law potentials. Some of these models can alleviate the ‘fine tuning’ problem which faces the cosmological constant.     

Conformally flat tilted Bianchi Type-V cosmological models in general relativity

We have investigated two conformally flat tilted Bianchi Type-V cosmological models in general relativity. To get a determinate solution, we have assumed a supplementary conditionA =B ⁿ between metric potentials wheren is a constant. The behaviour of the model forn = 2 is discussed in detail. Various physical and geometrical aspects of the models are also discussed.     

Conformally coupled scalar field solutions and the cosmological constant

Solutions are presented for a scalar field coupled conformally to Einstein gravity with a nonvanishing cosmological constant, in the case that the spacetime metric is spatially homogeneous and isotropic. Since the cosmological constant destroys the conformal invariance of the action, these solutions cannot be obtained by solving the flat space wave equation for the scalar field. It turns out that the metric is determined entirely by the cosmological constant, while the scalar field acquires an apparent mass squared which is proportional to the cosmological constant. It is conjectured that the cosmological constant in the universe at present may thus be disguised as the mass of some scalar field.     

A class of stationary rotating string cosmological models

We obtain a one parameter class of stationary rotating string cosmological models of which the well-known Gödel universe is a particular case. By suitably choosing the free parameter function, it is always possible to satisfy the energy conditions. The rotation of the model hinges on the cosmological constant which turns out to be negative. String-dust distribution in Gödel-type universes is also briefly discussed.     

Conformal Invariance, Accelerating Universe and the Cosmological Constant Problem

We investigate a conformal invariant gravitational model which is taken to hold at early universe. The conformal invariance allows us to make a dynamical distinction between the two unit systems (or conformal frames) usually used in cosmology and elementary particle physics. In this model we argue that when the universe suffers phase transition, the resulting mass scale introduced by particle physics should have a variable contribution to vacuum energy density. This variation is controlled by the conformal factor which is taken as a dynamical field. We then deal with the cosmological consequences of this model. In particular, we shall show that there is an inationary phase at early times. At late times, on the other hand, it provides a mechanism which makes a large effective cosmological constant relax to a sufficiently small value. Moreover, we shall show that the conformal factor acts as a quintessence field that leads the universe to accelerate at late times.     

Electromagnetic field with induced massive term: Case with scalar field

We consider an interacting system of massless scalar and electromagnetic fields, with the Lagrangian explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the electromagnetic field equation acquires an additional term, which in some cases is proportional to the vector potential of the electromagnetic field. This equation can be interpreted as the equation of motion of photon with induced nonzero rest-mass. This system of interacting fields is considered within the scope of Bianchi type-I (BI) cosmological model. It is shown that, as a result of interaction the isotropization process of the expansion takes place.     

Anisotropic Bianchi-I universe with phantom field and cosmological constant

We study an anisotropic Bianchi-I universe in the presence of a phantom field and a cosmological constant. Cosmological solutions are obtained when the kinetic energy of the phantom field is of the order of anisotropy and dominates over the potential energy of the field. The anisotropy of the universe decreases and the universe transits to an isotropic flat FRW universe accommodating the present acceleration. A class of new cosmological solutions is obtained for an anisotropic universe in case an initial anisotropy exists which is bigger than the value determined by the parameter of the kinetic part of the field. Later, an autonomous system of equations for an axially symmetric Bianchi-I universe with phantom field in an exponential potential is studied. We discuss the stability of the cosmological solutions.      

Two-component nonlinear Schrödinger models with a double-well potential

We introduce a model motivated by studies of Bose-Einstein condensates (BECs) trapped in double-well potentials. We assume that a mixture of two hyperfine states of the same atomic species is loaded in such a trap. The analysis is focused on symmetry-breaking bifurcations in the system, starting at the linear limit and gradually increasing the nonlinearity. Depending on values of the chemical potentials of the two species, we find numerous states, as well as symmetry-breaking bifurcations, in addition to those known in the single-component setting. These branches, which include all relevant stationary solutions of the problem, are predicted analytically by means of a two-mode approximation, and confirmed numerically. For unstable branches, outcomes of the instability development are explored in direct simulations.     

General relativity,the massless scalar field,and the cosmological constant

For gravity coupled to a neutral, massless scalar field, Wyman suggested a method of solution in power series valid provided the scalar field depends only on time. In this work we generalize his approach to nonzero cosmological constant.