On a Stationary Cosmology in the Sense of Einstein's Theory of Gravitation

A world is to be considered stationary in the sense of general relativity if the coefficients of its metric are independent of time in a coordinate system in which the masses are at rest on average. The remark on the system of coordinates is important because time itself is no invariant notion but is taken only in the sense of proper time. Our definition is unique, in the form given above. On the other hand it is also possible to have points where no matter is present. At such points we may place a test body of infinitesimally small mass and analyse whether it remains at rest in our coordinate system. A necessary and sufficient condition for this is that the time lines of our coordinate system are geodesics. Therefore the static solution given by de Sitter is not an example of a stationary world. The Schwarzschild line element which, from a cosmological point of view, is a world with a single central body can also not be considered a stationary solution. Indeed, there are no stationary solutions which are also spherically symmetric for the original field equations. The only such solution for the cosmological equations is Einstein's cylinder world. It is, to my knowledge, the only stationary world known so far. In that case the average matter density and the total mass of the world has to have a well defined value given by the cosmological constant which doubtless would be purely coincidental and is thus not a satisfactory assumption. In the following we shall discuss a new solution which is in accord with the original field equations without the need of an a priori relation between mass and cosmological constant. However, we shall find that its mass cannot be less than the mass of the cylinder world.     

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.     

Cosmological Model with Ω M -Dependent Cosmological Constant

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

一类宇宙模型的稳定性

研究了一类Einstein-Kartan宇宙模型的稳定性.分别讨论了宇宙模型对于参量λ和k的变化.在λ=0附近,宇宙模型相对于λ的变化是不稳定的;在λ=β=0附近,宇宙对于k的变化也是不稳定的.因此,在考虑合理的宇宙模型时必须考虑非零的宇宙项. 关键词： 宇宙 模型 广义相对论     

Neutrino Oscillations in the de Sitter and the Anti-de Sitter Space-Time

General expressions of the neutrino oscillation phase in the generally static space-time with spherical symmetry are given. The effect of the gravitational field on the oscillation length is embodied in the gravitational red shift factor. We find that a blue shift of the oscillation length takes place when the neutrino travels out of the gravitational field. Then, we discuss the variation of the oscillation length influenced by the cosmological constant. In the de Sitter space-time, the positive cosmological constant prolongs the oscillation length. And, in the anti-de Sitter space-time, the negative cosmological constant shortens it as expected.     

Implications of a non-zero cosmological constant on self-gravitating fermionic systems

The modified Thomas-Fermi equation of a degenerate self-gravitating fermion gas in the presence of a non-vanishing cosmological constant is studied. A restrictive relation between the mass of the bound cluster and the value of the cosmological constant is obtained for a given fermion mass.     

Algebraically special vacuum gravitational fields with a cosmological constant

A general view is given of the Petrov type II metric with a cosmological constant to an accuracy of two complex functions of three variables which are related by four differential equations. As a consequence the form of the metric is obtained for types III and N which are specified by one complex function satisfying three differential equations. A particular solution is given as an example of an accurate solution of type II with a cosmological constant. State University, Kazan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 102–108, June, 1996.     

Time-Dependent Density of Modified Cosmic Chaplygin Gas with Variable Cosmological Constant in Non-Flat Universe

In this paper we study modified cosmic Chaplygin cosmology with non-zero cosmological constant in non-flat Universe. By using well-known forms of scale factor we obtain time-dependent dark energy density by numerical analysis of non-linear differential equation and fitting curves. We use observational data to fix solution and discuss about stability of our system. First of all we consider cosmological constant as a constant in Einstein equation, and then study possibility of variable cosmological constant.     

Essay: Deconstructing the Cosmological Constant

Deconstruction provides a novel way of dealing with the notoriously difficult ultraviolet problems of four-dimensional gravity. This approach also naturally leads to a new perspective on the holographic principle, tying it to the fundamental requirements of unitarity and diffeomorphism invariance, as well as to a new viewpoint on the cosmological constant problem. The numerical smallness of the cosmological constant is implied by a unique combination of holography and supersymmetry, opening a new window into the fundamental physics of the vacuum.     

On the Existence of Conformally Coupled Scalar Field Hair for Black Holes in (Anti-)de Sitter Space

The Einstein-conformally coupled scalar field system is studied in the presence of a cosmological constant. We consider a massless or massive scalar field with no additional self-interaction, and spherically symmetric black hole geometries. When the cosmological constant is positive, no scalar hair can exist and the only solution is the Schwarzschild–de Sitter black hole. When the cosmological constant is negative, stable scalar field hair exists provided the mass of the scalar field is not too large.     

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.     

pp waves of conformal gravity with self-interacting source

Recently, Deser, Jackiw and Pi have shown that three-dimensional conformal gravity with a source given by a conformally coupled scalar field admits pp wave solutions. In this paper, we consider this model with a self-interacting potential preserving the conformal structure. A pp wave geometry is also supported by this system and, we show that this model is equivalent to topologically massive gravity with a cosmological constant whose value is given in terms of the potential strength.     

Axiomatic approach to the cosmological constant

A theory of the cosmological constant Λ is currently out of reach. Still, one can start from a set of axioms that describe the most desirable properties a cosmological constant should have. This can be seen in certain analogy to the Khinchin axioms in information theory, which fix the most desirable properties an information measure should have and that ultimately lead to the Shannon entropy as the fundamental information measure on which statistical mechanics is based. Here we formulate a set of axioms for the cosmological constant in close analogy to the Khinchin axioms, formally replacing the dependence of the information measure on probabilities of events by a dependence of the cosmological constant on the fundamental constants of nature. Evaluating this set of axioms one finally arrives at a formula for the cosmological constant given by , where G is the gravitational constant, m_e the electron mass, and α_el the low-energy limit of the fine structure constant. This formula is in perfect agreement with current WMAP data. Our approach gives physical meaning to the Eddington-Dirac large-number hypothesis and suggests that the observed value of the cosmological constant is not at all unnatural.     

Acceleration-enlarged symmetries in nonrelativistic space-time with a cosmological constant

By considering the nonrelativistic limit of de Sitter geometry one obtains the nonrelativistic space-time with a cosmological constant and Newton–Hooke (NH) symmetries. We show that the NH symmetry algebra can be enlarged by the addition of the constant acceleration generators and endowed with central extensions (one in any dimension (D) and three in D=(2+1)). We present a classical Lagrangian and Hamiltonian framework for constructing models quasi-invariant under enlarged NH symmetries that depend on three parameters described by three nonvanishing central charges. The Hamiltonian dynamics then splits into external and internal sectors with new noncommutative structures of external and internal phase spaces. We show that in the limit of vanishing cosmological constant the system reduces to the one, which possesses acceleration-enlarged Galilean symmetries.     

The spherically symmetric Einstein-scalar field system with positive and vanishing cosmological constant: a comparison

We review recent results concerning the spherically symmetric Einstein-scalar field system with positive cosmological constant. We do so by comparing with the classical results of Christodoulou concerning the asymptotically flat case (vanishing cosmological constant) and by discussing some of the issues which have emerged since the publication of our main results. Concerning the positive cosmological constant case, we also sketch an alternative proof of global in (Bondi) time existence, based on energy estimates, which is presumably more flexible and, consequently, amenable to generalizations; other potential improvements and generalizations of our main results are also discussed.     

Bianchi Type-V universe with a viscous fluid and Λ-term

We have studied the evolution of a homogeneous, anisotropic universe given by a Bianchi Type-V cosmological model filled with viscous fluid, in the presence of cosmological constant Λ. The role of viscous fluid and Λ-term in the Bianchi Type-V universe has been studied.      

The solution of the cosmological constant problem from the inhomogeneous equation of state — a hint from modified gravity?

The cosmological constant problem is studied in a two component cosmological model. The universe contains a cosmological constant of an arbitrary size and sign and an additional component with an inhomogeneous equation of state. It is shown that, in a proper parameter regime, the expansion of the universe with a large absolute value of the cosmological constant may asymptotically tend to de Sitter space corresponding to a small effective positive cosmological constant. It is argued that such a behavior can be regarded as a solution of the cosmological constant problem in this model. The mechanism behind the relaxation of the cosmological constant is discussed. A connection with modified gravity theories is discussed and an example of a possible realization of the cosmological constant relaxation in f(R) modified gravity is described.     

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.     

Canonical quantization of 1+1 dimensional gravity

Based on Polyakov's evaluation of the Fadeev-Popov determinant for (1+1)-dimensional gravity in the conformal gauge we formulate a canonical quantization in the synchronous gauge. We find that the system is describable as a quantum mechanical system of one degree of freedom. The quantization can be carried out and solved when any number of gauge fields are included. Scalar and spinor fields lead to new difficulties. For positive cosmological constant the geometry collapses as suggested by the classical system. For negative cosmological constant a more interesting behavior involving exponentially expanding and contracting universes occurs.Supported in part by NSF Grant No. PHy 78-26847.On leave from Tel Aviv University. Supported in part by the Israel Commission for Basic Research.