Dirac Equation in Lemaįtre—Tolman—Bondi Models

The Dirac equation is studied for a sufficiently large class of Lematre—Tolman—Bondi cosmological models. While the angular equation (whose solution is known) separates directly, the spatial and temporal dependence de-couples only after a suitable separation procedure. The separated time equation is integrated by series. The separated spatial equation still depends on an arbitrary function relative to the integration of the cosmological model.     

An exact bianchi type-V tilted cosmological model with matter and an electromagnetic field

We present a cosmological solution of the source-free Einstein-Maxwell equations with stiff matter and an electromagnetic null field, which is a locally rotationally symmetric tilted Bianchi type-V universe.     

On Wheeler's “rule of unanimity” in quantum cosmology

Counterexamples are given to Wheeler's rule of unanimity, which implies that every quantum solution for the problem of a closed universe within the framework of Einstein's field equations leads to a singularity. Bianchi IX universes filled with a perfect fluid with an equation of state of the type =(–1) (=const, between 1 and 2), quantized in the framework of the canonical scheme proposed by Lund and generalized by Demaret and Moncrief, are indeed shown to be nonsingular, apart from a set of measure zero of models including the closed Friedmann-Robertson-Walker models.     

Self-similar spacetimes: Geometry and dynamics

The nature and uses of self-similarity in general relativity are discussed. A spacetime may be self-similar (homothetic) along surfaces of any dimensionality, from 1 to 4. A geometric construction is given for all self-similar spacetimes. As an important special case, the spatially self-similar cosmological models are introduced, and their dynamical properties are studied in some detail: The initial-value problem is posed, the ADM formulation is established (when applicable), and it is shown that the evolution equations preserve a self-similarity of initial data. The existence of a conserved quantity is deduced from self-similarity. Possible applications to cosmology and singularities are mentioned. Supported in part by the National Science Foundation [GP-36687X].     

A critical density cosmological model with varying gravitational and cosmological “constants”

A cosmological model in which the universe has its critical density and the gravitational and cosmological constantsG and are time-dependent is presented. The model may possibly solve the horizon and monopole problems. It predicts a perpetually expanding universe in whichG increases and decreases with time in a manner consistent with conservation of the energy-momentum tensor. The model also allows the calculation of various cosmological parameters.     

Einstein-Cartan-Maxwell-bianchi type-V cosmological models

Exact cosmological solutions of the Einstein- Cartan-Maxwell equations with spin, stiff matter and an electromagnetic field for Bianchi type-V universes are obtained. A class of nonsingular solutions is presented. The most important characteristic of these solutions is that in one case the effect of the electromagnetic field is to reduce the value of the minimum volume while in another case there exists the possibility of enlarging this value arbitrarily.     

Causality in Inflationary Universes with Positive Spatial Curvature

We show that in the case of positively-curved Friedmann-Lemaître universes (k = +1), an inflationary period in the early universe will for most initial conditions not solve the horizon problem, no matter how long inflation lasts. It will only do so for cases where inflation starts in an almost static state, corresponding to an extremely high value of , 1, at the beginning of inflation. For smaller values, it is not possible to solve the horizon problem because the relevant integral asymptotes to a finite value (as happens also in the de Sitter universe in a k = +1 frame). Thus, for these cases, the causal problems associated with the near-isotropy of the Cosmic Background Radiation have to be solved already in the Planck era. Furthermore both compact space sections and event horizons will exist in these universes even if the present cosmological constant dies away in the far future, raising potential problems for M-theory as a theory of gravity.     

Static universe in a modified brans-dicke cosmology

We derive a static model of the universe, where density and pressure are constant, but the gravitational constant and the cosmological term vary with time, by means of the Endo-Fukui modified Brans-Dicke theory.     

Nonstationary quantum mechanics. I. Time-irreversible noninstantaneous self-reduction to a stationary state of some quantal wave packets

It is shown that the formalism of quantum theory needs modification in the case of potential fields swiftly varying with time. The necessity of a time-irreversible master equation for such cases is discussed.The underlying idea is that any (sub)system will undergo a spontaneous transition to a state of definiteenergy in the process of separating spatially from the rest of the universe, assuming the universe is isolated and has a definite energy. This requires what might be termed a pragmatic interpretation of the wave function: If a composite, separated system is represented by a linear superposition of product states, we may say that the actual state of the composite system is represented by some particular component of the superpositionfor the purposes of statistical inferences relevant to each subsystem alone, but the entire superposition—and not the corresponding mixture of the product components—must be used to compute the statistics of correlations. The considerations are illustrated with thought experiments which are real enough to make the application of the usual quantum mechanical formalism possible. Cases of disagreement between conventional theory and experiment in the field of interest are indicated.     

Nonvacuum taub-type cosmological model

The Einstein universe is a simple model describing a static cosmological spacetime, having a constant radius and a constant curvature, and, as is well known, it does not describe our universe. We propose a model which is an extension of Einstein's. Our metric, havingR × S ³ topology, describes a nonisotropic homogeneous closed (finite) universe of Bianchi type IX. This metric is similar to that of Taub, but is simpler. Unlike the Taub solution (which is a cosmological extension of the NUT solution), however, the universe described by our metric contains matter. Like the Taub metric, our metric has two positive constants (, T). The gravitational red shift calculated from our metric is given. Similarly to the Schwarzschild metric, which has a singularity atr = 2m, this metric has the same kind of singularity att = 2. The maximal extension of the coordinates in our metric is fairly analogous to that of the Schwarzschild metric.     

К ВОПРОСУ О ФОТОПРОВО ДИМОСТИ ФОТОГРАФИЧЕСКОЙ ЭМУ ЛьСИИ

) . , , , ; , , . . , .     

Does μ<1 imply that the universe will expand forever?

The issue of whether the present observational evidence that the mean mass density of the universe is less than the critical density (i.e., <1) implies an infinite future expansion of the universe is discussed. Although in conventional cosmological scenarios <1 necessarily leads to a universe that will grow infinitely old, this conclusion can be avoided in ways which are reasonably natural. One of these is to assume the existence of a small negative cosmological constant. Another way is to postulate the existence of unstable fields with a long time scale for the onset of the instability. An example is a scalar field with a negative squared mass and ¦m¦10^–32eV. Other examples include fields for which the instability is generated by quantum corrections in curved space-time. All of these are capable of halting the expansion of an open universe and forcing it to recollapse into a big crunch.This essay received the fourth award from the Gravity Research Foundation for the year 1986—Ed.     

The relation between the relativistic 5D Wesson theory and the Newtonian variable mass theory

The existence of Newtonian analogs to spatially homogeneous and isotropic cosmological models of the relativistic 5D Wesson variable mass theory is investigated. By treating the continuous universe matter creation process by the methods of standard hydrodynamics, it is shown that classical analogs are obtained only if the cosmological constant is null and the spatial curvature is positive.     

Uniform Newtonian models with variable mass

A Newtonian version of the spatially homogeneous and isotropic cosmological models with variable mass is presented. Under the assumption that the mass variation is a strict cosmological effect, its influence on the evolution of the scale function is established for the case of a dust-filled universe. Unlike the usual Newtonian models the present value of the deceleration parameter (q 1) obtained from the luminosity distance versus redshift relation can be fitted for a time-decreasing mass. It is also shown that the hyperbolic, parabolic or elliptic character of the fluid motion can be modified along the expansion. Likewise, a Friedmann-type equation with a variable curvature term indicates that in the frame-work of a full geometric variable mass theory, the same may occur with the open, flat or closed character of the universe spatial section.     

MultipletSO(n+1) scalar fields driving eternal expansion in closed (D+1)-dimensional FLRW cosmologies

The possibility of having a de Sitter asymptotic stage free of choice of the value of the positive cosmological constant (no critical ) is analyzed in a closed FLRW universe which starts from a quiescent phase of evolution and ends into a textured phase by taking into account multipletSO(n+1) scalar fields.On leave of absence from Universidade Federal do Rio de Janeiro, RJ, Brazil     

Exact solutions in Brans-Dicke theory with bulk viscosity

The effect of bulk viscosity on the evolution of the homogeneous and isotropic cosmological models in the Brans-Dicke theory of gravitation is studied. Solutions are found, with a baratropic equation of state, a time-independent bulk viscosity, the gravitational constant inversely proportional to the age of the universe, and the mass of the universe (in the closed model) proportional to the square of its age; the expansion factor is a linear function of the cosmological time. For flat space, power law expansions are found, among them one that is related to extended inflation.     

Elementary physical approach to Mach's principle and its observational basis

It is shown that Mach's principle and the general principle of relativity are logical consequences of a materialistic postulate and that general relativity implies the validity of Mach's principle for a static (or quasistatic) homogeneous and isotropic universe, spatially self-enclosed. The finite velocity of propagation of gravitational field does not imply a retardation of inertial forces due to the distant masses and therefore does not exclude the validity of Mach's principle. Similarly, the experimentally verified isotropy of inertia is compatible with this principle. The recent observational evidence of very high isotropy of the actual universe proves that the anti-Machian Gödel world model must be rejected as a nonphysical one. This suggests the possibility of a renaissance of Einstein's first cosmological model by considering-in the spirit of an older idea of Herbert Dingle-a superlargescale quasistatic universe consisting of an unknown number of statistically oscillating regions similar to our own, momentarily expanding, metagalaxy.     

Effects on the Structure of the Universe of an Accelerating Expansion

Recent experimental results from supernovae Ia observations have been interpreted to show that the rate of expansion of the universe is increasing. Other recent experimental results find strong indications that the universe is flat. In this paper, I investigate some solutions of Einstein's field equations which go smoothly between Schwarzschild's relativistic gravitational solution near a mass concentration to the Friedmann-Lemaître expanding universe solution. In particular, the static, curved-space extension of the Lemaître-Schwarzschild solution in vacuum is given. Uniqueness conditions are discussed. One of these metrics preserves the cosmological equation. We find that when the rate of expansion of the universe is increasing, space is broken up into domains of attraction. Outside a domain of attraction, the expansion of the universe is strong enough to accelerate a test particle away from the domain boundary. I give a domain-size–mass relationship. This relationship may very well be important to our understanding of the large scale structure of the universe.     

Anisotropic cosmological models of Bianchi types III and V in Lyra's geometry

Exact solutions to Einstein's equations are presented in vacuum and in the presence of stiff matter for spatially homogeneous cosmological models of Bianchi types type III and V in the normal gauge for Lyra's geometry. Solutions represent anisotropic cosmological universes which contract from infinite volume at the initial time singularityT=0 to zero volume asT. Some physical properties of the models are also discussed.     

Bianchi type-I solutions for modified Brans-Dicke cosmology

Cosmological dust solutions have been obtained in Bianchi type-I homogeneous space for Brans-Dicke modified theory by the condition of the cosmological parameter ().