Hidekazu Nariai

On the Dissipation of Primordial Turbulence in the Expanding Universe

The growth of primordial density contrasts and their separation from the general expansion of the universe are the first step in the course of galaxy formation, which has been attempted to describe by various mechanisms. The epoch of the separation depends on the amount of density contrasts at some epoch, which must be more than several billion years ago. In the case of ~ravitational instability there arises some lower limit for the initial density contrast which cannot be explained by the statistical origin.> It has been expected, on the other hand, that thermal instability may play an important role at an early stage of the growing of the density contrasts.),S) This mechanism can be effective, only if heating and cooling balance each other so as to keep matter at high temperature (at least higher than 10 °K) at the pregalactic stage. However, if no heating source of matter exists, the matter temperature Tm downs faster than the radiation temperature Tr after the epoch of the decoupling at Tr::::::4000°K. > The rotational and peculiar motions of the galaxies in the present state suggest us a possibility that enormous turbulent motions have existed at the pregalactic stage. Weizsacker> and Gamow> insisted upon its importance in the problem of galaxy formation. To meet with this, the theory of turbulence in the expanding universe has been developed by one of the authors (H. N.).>•*> On the basis of a more realistic picture for the hot universe motivated by the discovery of cosmic black-body radiation, Ozernoi and Chernin> have recently

Hydrodynamic Calculations of Spherical Gravitational Collapse in the Scalar-Tensor Theory of Gravity

Hydrodynamic equations for spherical gravitational collapse in the scalar-tensor theory of gravity are approximated by finite-difference equations. The dynamical motion of a gaseous sphere is calculated numerically on the assumption that the sphere consists of a perfect gas without energy flow and, therefore, its total mass is conserved. In order to avoid the difficulty of ~atching of the metric and scalar fields at .the surface of the gaseous sphere, the sphere is divided into two parts, i.e., a central core and an extended tenuous atmosphere. In the collapsing core, scalar waves are generated around its central region at the final stage, but their effect is not so large as to deviate various physical quantitiEs appreciably from those to be obtained in the general relativistic treatment, except in the inner-most region of self-closure.

On the invariant spatial distance in a curved space-time with spherical symmetry.

Two kinds of the lnvariant spatial distance based on the geodesic deviation of null-geodesics in a curved space-time with spherical symmetry are studied. There is an intimate connection between the definability of these two spatial distances and the space-time structure. This assures adequacy that the concept of invariant spatial distance could be a powerful tool in the researches on the space-time structure. Results can be utilized in the problem of the allowable mean value for the invariant spatial distances among several observers and for other problems. (auth)

On some peculiar role of the cosmological constant in the general theory of relativity and in the Schrodinger theory of non-symmetric field.

ABS>The peculiar role of the so-called cosmological constant LAMBDA is investigated from two alternative standpoints of the general theory of relativity and the Schrodinger theory of nonsymmetric fields. It is shown that, in spite of a rather drastically different character of the latter theory from the former, there exists a peculiar solution whose existence is assured by the role of LAMBDA and whose physical meaning is equivalent to that of Bertottis solution in general relativity. (auth)

The Behavior of a Massless Scalar Field in a Closed Universe

In order to see how the propagation character of a long-range field in a closed universe depends on its topological property, the. dynamical behavior of a massless scalar field ina closed universe with a definite (spherical or elliptic) topology is studied. It is shown that the difference of topology gives no serious influence upon the propagation character of the field. However, the retarded Greens function obtained here is superior to the one which we derived in a previous paper without taking account of the topology of the universe. In fact, we must use the former Greens function when we examine whether Brans and Dickes world models with spherical or elliptic topology are compatible with their interpretation of Machs . principle.

BEHAVIOR OF THE CENTRAL REGION OF A COLLAPSING STAR WITH SPHERICAL SYMMETRY AND PRESSURE GRADIENT

The behavior oi the central region of a collapsing star with spherical symmetry and a finite pressure gradient is studied from the standpoint of boundary conditions at the center r=O. In the case of adiabatic collapse, Einsteins equations supplemented by an equation of state are reduced to four independent equations for five unknown functions of the time variable t only. This arbitrariness is analogous to that in the selection of initial Cauchy data at t=O in the Misner-Sharp approach and it enables us to construct a variety of models for the central region regular at all times. W c also touch upon the case of non-adiabatic collapse by introducing a suitable parameter whose n:~ciprocal stands for the time-scale of the energy flow near r=O.

QUANTIZATION OF THE GRAVITATIONAL FIELD IN THE EXPANDING UNIVERSE

An attempt is made to quantize, in the linear approximation, the gravitational field in the expanding universe, from the standpoint of canonical formalism. By using a transformation function and decomposing suitably the field operator into positive and negative frequency parts, explicit forms of the four- dimensional commutation function and the propagation function are derived in the case of three special world models. There appears the difficulty of divergence term in the propagation function, with the exception of one model. The propagation function, however, satisfies the relation between Hadamards elementary solution and the propagation function postulated by De Witt and Brehme. In addition, a connection between the propagation function and the time-ordered product of field operators is established by introducing a state of quasi-vacuum in parallel with our decomposition mentioned above. Finally, detailed discussions of several difficulties are given in connection with the problem of causality. It is suggested from the analysis that the quantum theory and the general relativity cannot rigorously be compatible, so far as the hypothesis of the expanding universe is concerned. (auth)

Generation of Sound from Primordial Cosmic Turbulence

From the standpoint of the turbulent origin of the formation of galaxies, it is important whether the primordial cosmic turbulence can survive up to the necessary epoch against acoustic decay. This is a preliminary report of our new formalism for attacking the problem.

On the Generatin of Sound from the Primordial Turbulence in an Expanding Universe

In order that galaxies may be formed from the primordial turbulence in a big-bang universe, the cosmic turbulence with suitable scales must survive up to the decoupling epoch of matter from radiation against its decay due to the generation of sound as envisaged by Lighthill and Crighton. To attack the problem with due consideration of the effect of cosmic expansion neglected in the Lighthill-- Crighton theory, the generation of sound from the cosmic turbulence is dealt with by constructing the appropriate retarded Oreens function in which all significant influences of the cosmic expansion upon the propagation of sound waves to be generated are woven. rt is shown that the expanding turbulent fluid is inevitably of a diffusive nature in such a way that its physical radius is equal to the acoustical event horizon. The latter situation means that the retardation effect is essential in the evaluation of the intensity of sound at the center of the turbulent fluid sphere, while the effect was discarded in the Crighton formula for a static diffusive medium. In other words, the formalism is superior to Crightons for the examination of the aforementioned problem. (auth)

On a New Approach to Cosmology

An attempt is made to develop a new theory of cosmology based on a scalar field, in view of several weak points proper to the general relativistic cosmology. In our treatment,. a kind of correspondence principle plays the important role, together with the consideration of the scope of applicability of general relativity. Our cosmological field equation thus proposed not only has an intimate linkage with Einsteins equations, but also satisfies Machs relation for the universe as a whole in a covariant and intrinsic manner.