Showing papers on "Big Rip published in 1971"

Quantized fields and particle creation in expanding universes. ii.

Abstract: Spin-0 fields of arbitrary mass and massless fields of arbitrary spin are considered. The equations governing the fields are the covariant generalizations of the special-relativistic free-field equations. The metric, which is not quantized, is that of a universe with an expanding (or contracting) Euclidean 3-space. The spin-0 field of arbitrary mass is quantized in the expanding universe by the canonical procedure. The quantization is consistent with the time development dictated by the equation of motion only when the boson commutation relations are imposed. This consistency requirement provides a new proof of the connection between spin and statistics. We show that the particle number is an adiabatic invariant, but not a strict constant of the motion. We obtain an expression for the average particle density as a function of the time, and show that particle creation occurs in pairs. The canonical creation and annihilation operators corresponding to physical particles during the expansion are specified. Thus, we do not use an S-matrix approach. We show that in a universe with flat 3-space containing only massless particles in equilibrium, there will be precisely no creation of massless particles as a result of the expansion, provided the Einstein field equations without the cosmological term are correct. Furthermore, in a dust-filled universe with flat 3-space there will be precisely no creation of massive spin-0 particles in the limit of infinite mass, again provided that the Einstein field equations are correct. Conversely, without assuming any particular equations, such as the Einstein equations, as governing the expansion of the universe, we obtain the familiar Friedmann expansions for the radiation-filled and the dust-filled universes with flat 3-space. We only make a very general and natural hypothesis connecting the particle creation rate with the macroscopic expansion of the universe. In one derivation, we assume that in an expansion of the universe in which a particular type of particle is predominant, the type of expansion approached after a long time will be such as to minimize the average creation rate of that particle. In another derivation, we use the assumption that the reaction of the particle creation back on the gravitational field will modify the expansion in such a way as to reduce, if possible, the creation rate. This connection between the particle creation and the Einstein equations is surprising because the Einstein equations themselves played no part at all in the derivation of the equations governing the particle creation. Finally, on the basis of a so-called infinite-mass approximation, we argue that in the present predominantly dust-filled universe, only massless particles of zero spin might possibly be produced in significant amounts by the present expansion. In this connection, we show that massless particles of arbitrary nonzero spin, such as photons or gravitons, are not created by the expansion, regardless of its form.

Energy in the Universe

Abstract: Energy flows in the universe are described and the genesis of the various kinds of energy is discussed. The process by which energy is channeled in the cosmos are discussed with implications for the earth highlighted.

Possible evidence for the existence of antimatter on a cosmological scale in the universe.

Abstract: Initial results of a detailed calculation of the cosmological gamma-ray spectrum from matter-antimatter annihilation in the universe. The similarity between the calculated spectrum and the present observations of the gamma-ray background spectrum above 1 MeV suggests that such observations may be evidence of the existence of antimatter on a large scale in the universe.

Perturbations in an anisotropic homogeneous universe.

Abstract: In an anisotropic homogeneous cosmological model, the growth of the matter-density perturbations is a kinetic effect of the motion of matter in an external field, in accord with the concepts of Lifshitz and Khalatnikov[ 1 l concerning the vacuum stage. Using this result, we find the law governing the growth of small perturbations and the general solution for finite perturbations of matter without pressure, p = 0. We show that in anisotropic models the perturbations increase 3-5 times faster than in the isotropic model (see formula (5)). Long-wave perturbations in a medium with P = t:/3 increase 2-3 times faster (see formula (9)). The law governing the variation of the amplitude ofacoustic and gravitational waves is also explained.

Antimatter in the Universe

Abstract: The models of nucleosynthesis discussed in this article could give clues to the possible existence of aggregations of antimatter in the universe.

On the instability in universe

Abstract: With coordinate conditions which are different from Lifshitz’s ones it is investigated the instability in a universe model locally nonhomonogeneous which is the generalization of Shirokov and Fisher’s model. The general equation for the density contrast E is obtained. For the gravitational instability in the cases of uniform models containing matter and blackbody radiation and of the oscillating model of Rosen one gets E ~ t4/3 and respectively. The general equation for thermal instability in the later stages of cosmic evolution is also obtained. Basing on different investigations about the thermal conditions of intergalactic matter the numerical values of the growth rate of the density contrast are calculated. All those results show the important role of . thermal instability in the galaxy formation. RESUME. Avec des conditions de coordonnees qui sont différentes de celles de Lifshitz, on a etudie l’instabilité d’un modele d’Univers localement non-uniforme qui est la generalisation du modele de Shirokov et Fisher. On a etabli l’équation générale pour la variation relative de densité E. Pour l’instabilité gravitationnelle du modele contenant matiere et rayonnement et du modele oscillant de Rosen, on a montre que E ~ t4/3 et E ’" t2 respectivement. L’équation générale pour l’instabilité thermique dans les périodes récentes de 1’evolution cosmique est aussi déterminée. On a calcule les valeurs numeriques du degré de croissance de la variation relative de densite en se basant sur les différentes investigations concernant les conditions thermiques de la matiere intergalactique. Tous ces resultats montrent le role important de l’instabilité thermique dans la formation des galaxies. ’ (*) Laboratoire de Physique Théorique associe au C. N. R. S.

A universe embedded in a five-dimensional flat space

Abstract: Since a homogeneous isotropic universe can be embedded in a flat space of five dimensions, the question is considered under what conditions a more general universe can be embedded in a five-dimensional flat space. On the assumption that the deviation from homogeneity is small, it is found that real inhomogeneities can occur only in the case of a universe filled with radiation, or a universe containing at least two different substances with different equations of state, as for example radiation and matter. In the case of a radiation-filled universe, the inhomogeneities can be of arbitrary size and can conceivably be the precursors of galaxies.