Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 1974"

Quantization of a coupled Fermi field and Robertson-Walker metric

Abstract: The combined Dirac field and Robertson-Walker metric system is quantized in a Heisenberg picture. One of the Einstein equations is implemented as a constraint on the state vectors and leads to a spectrum for the allowed values of the mass of the spinor field.

On the Average Effect of a Highly Turbulent Gravito-Hydrodynamic Field in the Hadron Era of the Universe

Abstract: An attempt is made to give a physi-cal basis for our modification of Einstein's gravita­ tional equations, which has been proposed in a previous paper to arrive at an isotropic model-universe that may bounce in the hadron era, tends rapidly to the Friedmann universe and remains regular with respect to the excitation of gravitational and rotational waves. The basic idea lies in reinterpreting the modified field equations as those for the mean-value field of a highly turbulent gravito-hydrodynamic field (obeying Einstein's equations) whose substratum is dominated by the hadronic matter, with large density fluctuation. In the case where the mean-value metric represents the regular model-universe, it is shown that, so far as the bounce epoch of the universe. is concerned, three characteristic mean-value quantities specifying metric, velocity and density fluctuations are compatible with the basic idea. Sev­ eral problems to be pursued further are also touched upon. § I. Introduction In a previous paper1> (which is referred to as [IJ hereafter), a phenomenol­ ogical modification -of Einstein's gravitational equations has been proposed, in order to arrive at a regular isotropic model-universe which asymptotically tends to the Friedmann universe and remains regular with respect to the excitation of gravitational and rotational waves. It has been shown that the substratum at its most compressed stage must be dominated by hot hadronic matter at an extremely

Tetrad field equations and a generalized Friedmann equation

Abstract: The tetrad field equations of general relativity discussed in previous articles are applied to Robertson-Walker cosmological models. A generalized Friedmann equation is derived and some of its consequences are discussed.

The cosmological effects of generalized field equations in relativity

Abstract: An autonomous system of equations, describing uniform cosmological models, is formulated by using the perfect fluid approximation of Einstein’s equations These equations contain an arbitrary function related to the matter content of the universe, which may include negative energy fields This function, designated α , is assumed to depend on the density and expansion rate of the universe only Geometrical methods of analysis are used to study the behaviour of all models described by this system The analysis shows that there are only three possible modes of behaviour that can be exhibited by a uniform universe Examples of the first two classes are well known in the ‘big-bang’ and ‘steady-state’ theories However, it is shown that the familiar theories are not unique, but an infinite number of both such types of model exist for various α It is also shown that all steady-state models in an expanding universe are stable The third class of model, associated with periodic behaviour, is of two types The first is demonstrated by a universe which oscillates between expansion and contraction but never achieves infinite density The second consists of ever-expanding (or contracting) models in which the density and expansion rate oscillate between finite values These latter models possess evolutionary characteristics on ‘short’ time-scales, while satisfying the ‘perfect cosmological principle’ in the large, and only arise in the presence of gross non-linearities introduced by the function α Both the periodic and steady-state classes occur only in the case of negative energy fields