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Showing papers on "Particle horizon published in 1980"


Journal ArticleDOI
TL;DR: The physical interpretation of perturbations of homogeneous, isotropic cosmological models in the early Universe, when the perturbation is larger than the particle horizon, is clarified by defining a complete set of gauge-invariant variables as discussed by the authors.
Abstract: The physical interpretation of perturbations of homogeneous, isotropic cosmological models in the early Universe, when the perturbation is larger than the particle horizon, is clarified by defining a complete set of gauge-invariant variables. The linearized perturbation equations written in these variables are simpler than the usual versions, and easily accommodate an arbitrary background equation of state, entropy perturbations, and anisotropic pressure perturbations. Particular attention is paid to how a scalar (density) perturbation might be generated by stress perturbations at very early times, when the non-gauge-invariant perturbation in the density itself is ill-defined. The amplitude of the fractional energy density perturbation at the particle horizon cannot be larger, in order of magnitude, than the maximum ratio of the stress perturbation to the background energy density at any earlier time, unless the perturbation is inherent in the initial singularity.

2,114 citations


Journal Article
TL;DR: A quantum theory of irrotational perturbations of an ideal fluid in a spatially flat isotropic homogeneous cosmological model is constructed by Lifshitz and Pitaevskii as discussed by the authors.
Abstract: A quantum theory of irrotational perturbations of an ideal fluid in a spatially flat isotropic homogeneous cosmological model is constructed Two gauge-invariant canonically conjugate scalars are obtained that describe the evolution of the two physical degrees of freedom of irrotational perturbations of the matter in an expanding universe; they are analogs of the velocity potential and the density perturbation in a stationary nongravitating medium (EM Lifshitz and L P Pitaevskii, Statistical Physics, Part 2, 1978, section24) A Lagrangian and an equation of motion of second order are obtained Canonical quantization is performed, and the concept of phonons (sound quanta in a nonstationary universe) is introduced Conformal noninvariance of sound waves in an isotropic universe is proved It is shown that the mechanism of spontaneous production of phonons in the process of the cosmological expansion is the cause of the formation of the initial spectrum of adiabatic perturbations of the matter density in an isotropic Friedmann universe In the subsequent evolution in the stage after hydrogen recombination in an expanding universe the long-wavelength density fluctuations may lead to the formation of galaxies and clusters of galaxies Estimates are made of the spectrum of the primordial density fluctuations It it shown thatmore » they are in agreement with the requirements imposed on the initial spectrum by the adiabatic theory of the origin of galaxies« less

50 citations


Journal ArticleDOI
TL;DR: It is argued that the small horizon when the universe was close to the Planck temperature restricted the possible energies of elementary particles, preventing them from being in full thermal equilibrium.

33 citations


Journal ArticleDOI
TL;DR: In the context of nucleosynthesis compatibility, this article showed that the universal lepton numbers still suggest an open universe, even in the case of the big-bang nucleosynthetic compatibility.
Abstract: Big-bang nucleosynthesis per se cannot decide if the universe is open or not. Present gauge theories of elementary particles favour, on several grounds, low values (much less than unity) of the universal lepton numbers. These values, in the context of nucleosynthesis compatibility, still suggest an open Universe (13

26 citations


Journal ArticleDOI
TL;DR: In this paper, three basic questions about the physics of the early universe are briefly discussed: the origin of the entropy, the amplitude of initial fluctuations, and the overall homogeneity of the universe.
Abstract: Three basic questions about the physics of the early universe are briefly discussed: the origin of the entropy, the amplitude of initial fluctuations, and the overall homogeneity of the universe.

15 citations


Journal ArticleDOI
TL;DR: In this article, the amount of particle pairs created in a 3-flat Robertson-Walker universe with an expansion law for the early Universe is calculated exactly when a homogeneous electromagnetic field is present.
Abstract: The amount of particle pairs created in a 3-flat Robertson-Walker Universe with an expansion law for the early Universe is calculated exactly when a homogeneous electromagnetic field is present. Under some restrictions a time-dependent particle creation rate is found. Finally it is shown that the low-frequency part of the cosmological 2.7K background radiation can be identified with the stationary electromagnetic field discussed before. According to this a large amount of particles of the order of the number of particles in the Universe should be created out of the vacuum in the immediate neighbourhood of the 'big bang'.

12 citations


Book
01 Jan 1980
TL;DR: In this paper, the authors describe the evolution of the universe in terms of the number of galaxies, the distribution of galaxies in space, and the contribution of intergalactic material in the universe.
Abstract: I: The Metagalaxy out to a Distance of One Gigaparsec.- 1. Distance Scale.- 1.1 Cepheids.- 1.2 H II Regions.- 1.3 Luminosity Classes.- 1.4 The Diameter - Luminosity Relation.- 1.5 Groups of Galaxies.- 2. The Distribution of Galaxies in Space.- 2.1 The Local Group.- 2.2 The Nearby Groups.- 2.3 The Virgo Cluster.- 2.4 The Coma Cluster.- 2.5 Rich Clusters.- 2.6 Superclusters.- 2.7 Gradients.- 3. The Expansion of the Universe.- 3.1 The Nature of the Expansion.- 3.2 The Value of the Hubble Constant.- 4. Nearby Intergalactic Matter.- 4.1 Optical Observations.- 4.2 21-cm Radio Observations.- 4.3 X-Ray Observations.- 5. The Density of the Universe.- 5.1 The Contribution of Galaxies.- 5.2 The Contribution of Intergalactic Material.- 5.3 Other Contributions.- 5.4 The Density of the Universe.- 6. The Age of the Universe.- II: Spaces with Constant Curvature.- 7. Locally Euclidean Spaces.- 7.1 Natural Frame.- 7.2 The Riemann-Christoffel Tensor.- 7.3 Locally Euclidean Space.- 7.4 Development.- 7.5 Holonomy Groups.- 7.6 Fundamental Polyhedron.- 7.7 Representing Locally Euclidean Space in Euclidean Space.- 7.8 The Various Types of Locally Euclidean Space.- 8. Locally Non-Euclidean Spaces.- 8.1 First Order Representation.- 8.2 Second Order Representation.- 8.3 Development Along a Curve.- 8.4 Geodesic Surfaces.- 8.5 The Riemann-Christoffel Tensor.- 8.6 Riemannian Curvature.- 8.7 General Properties of Locally Non-Euclidean Spaces.- 8.8 The Various Types of Locally Non-Euclidean Spaces.- 9. Spherical and Hyperbolic Spaces.- 9.1 Geodesic Representation.- 9.2 Central Representation.- 9.3 Other Representations.- 9.4 Appendix.- III: Model Universes.- 10. Uniform Relativistic Model Universes.- 10.1 The Equations of General Relativity.- 10.2 Dingle's Equations.- 10.3 Cosmological Solution.- 10.4 The Robertson-Walker Metric.- 10.5 The Friedmann Universes.- 10.6 Radiation-Filied Universes.- 11. Theory of Observations in the Relativistic Zone.- 11.1 Motion of Photons.- 11.2 Spectral Ratio.- 11.3 Travel Time of Photons.- 11.4 Age of the Universe.- 11.5 Diameter.- 11.6 Luminosity.- 11.7 Brightness.- 11.8 Number of Observable Objects.- 11.9 Other Parameters.- 12. The Cosmological Constant.- 12.1 The (q, ?) Diagram.- 12.2 Evolution of the Universe.- 12.3 Age of the Universe.- 12.4 The Hubble Diagram.- 13. Cosmological Horizons.- 13.1 Particle Horizon.- 13.2 The Event Horizon.- 13.3 The Absolute Horizon.- 13.4 The Determination of Horizons.- IV: The Metagalaxy in the Relativistic Zone.- 14. The Hubble Diagram for Galaxies.- 15. Distant Intergalactic Material.- 15.1 Neutral Hydrogen.- 15.2 Ionized Hydrogen.- 16. Radio Galaxies and Quasars.- 16.1 Basic Data.- 16.2 Number Counts.- 16.3 Distribution and Luminosity Function.- 16.4 Isotropy of Extragalactic Radio Sources.- 16.5 Test of Closure.- 17. The Cosmic Microwave Background.- 17.1 Description of the Cosmic Background.- 17.2 Cosmological Interpretation.- Numerical Constants.

7 citations


Journal ArticleDOI
Paul S. Henry1
29 Feb 1980-Science
TL;DR: An intuitive model for the expansion of the universe is developed in which special relativity is used to describe events seen by a hypothetical observer in a Lorentz frame of reference, which approximates an open universe with increasing accuracy as time evolves.
Abstract: An intuitive model for the expansion of the universe is developed in which special relativity is used to describe events seen by a hypothetical observer in a Lorentz frame of reference. The cosmic microwave background photons he sees are the red-shifted remnants of hot photons emitted from the matter flying rapidly away from him. This special relativistic model, also called the Milne model, represents the extreme case of a Friedmann (general relativistic) universe in the limit of vanishingly small density of matter. The special relativistic model approximates an open universe (one that expands forever) with increasing accuracy as time evolves.

5 citations


Journal ArticleDOI
TL;DR: In this article, the authors analyse the isotropization of homogeneous cosmological models including phenomenologically the contribution of vacuum polarization to the energy content of the universe and show that the combined effect of dissipative processes at early epochs and of vacuum at relatively late epochs guarantees the isotropy of the Universe at large times for arbitrary initial anisotropies, provided the universe expands forever and the vacuum has positive energy density and negative stresses with a sufficiently hard equation of state.
Abstract: We analyse the isotropization of homogeneous cosmological models including phenomenologically the contribution of vacuum polarization to the energy content of the Universe. The combined effect of dissipative processes at early epochs and of vacuum at relatively late epochs guarantees the isotropy of the Universe at large times for arbitrary initial anisotropies, provided the Universe expands forever and the vacuum has positive energy density and negative stresses with a sufficiently hard equation of state. Isotropy at the present epoch is secured by a negative deceleration parameter consistent with observation.

5 citations


Journal ArticleDOI
TL;DR: In this article, the Friedmann expansion of the universe has been studied in the context of the spectrum characteristics of nucleosynthesis, and the effect of the quantum and short-wave classical fluctuation to the expansion law has been considered.
Abstract: The chaotic Universe is considered, which is homogeneous and isotropic on the sealesL ≫L whereL is the scale of averaging. From the Einstein equations, the equations for the correlation functions have been obtained which describe the statistically chaotic model with the fluctuations of arbitrary amplitudeh. In the approximation of δ-correlated fluctuations andh≪1, the infinite set of coupled equations for the correlators closes and gives a self-consistent description of the inverse influence of the vortical and potential perturbations and gravitational waves with random initial phases on the Friedmann expansion of the Universe. For the state equationp=ne, the cosmological solutions have been foud.. They depend on the position of the maximum in the spectrum of the metric perturbations (λmax >ct or λmax 0.26 it goes below it. The effect of the finites ast → 0 long-wave fluctuations leads to an averaged quasi-isotropic solution. The contribution of the quantum and short-wave classical fluctuation to the expansion law is also considered. Their effect is equivalent to the contribution from an additional ultrarelativistic gas at corresponding energy density and pressure. In Paper II, the constraints on the degree of the chaos (the spectrum characteristics) of the Universe by the time of nucleosynthesis are obtained, which involve the observed helium abundance.

4 citations




01 Jul 1980
TL;DR: In this article, the cosmological constant λ(n) was introduced to measure the rest mass of all neutrino species as well as the age of the universe for the Friedmann universe, contrary to the age observed for the oldest stars in the Galaxy.
Abstract: Recent measurements of the spectrum of tritium decay electrons in the USSR suggest that electronic neutrinos may have a rest energy m/sub ..nu../c/sup 2/approx. =30 eV. Primordial neutrinos would then make a major contribution to the mean density of matter in the universe, enough for the universe to be closed. If future reactor and accelerator experiments should reveal that muonic and tau neutrinos have a mass of the same order, then one would infer an age of less than 10/sup 10/ yr for the Friedmann universe, contrary to the age observed for the oldest stars in the Galaxy. The contradiction can be removed by introducing the cosmological constant ..lambda... Conversely, measuring the rest mass of all neutrino species as well as the age of the universe would afford a unique opportunity to evaluate ..lambda...

Journal ArticleDOI
TL;DR: In this paper, it is suggested that gravity may not be asymptotically free at short distances because of the interaction of the graviton with matter, and the possibility of abnormally strong gravity at high energies or short distances is discussed in some detail.
Abstract: It is suggested that gravity may not be asymptotically free at short distances because of the interaction of the graviton with matter. If gravity indeed becomes strong at high energies, a revolutionary change of our present theory on the early universe would seem to be necessary. During the first extremely small fraction of a second in the big-bang universe, gravity would have been so strong that it might not have been described by Einstein's theory of general relativity. The possibility of abnormally strong gravity at high energies or short distances is discussed in some detail. A possible explanation is proposed for the nonvanishing mean baryon number density of the universe. It is also pointed out that the universe may well escape from the catastrophic singularity of Penrose and Hawking.

Book ChapterDOI
01 Jan 1980
TL;DR: The single mode of gravitational radiation that activates the Taub model universe has the longest possible wavelength that will fit into that universe and an amplitude just sufficient to curve the geometry up into closure, via its "effective" content of mass energy, both kinetic and potential as mentioned in this paper.
Abstract: The single mode of gravitational radiation that activates the otherwise empty Taub model universe has the longest possible wavelength that will fit into that universe and an amplitude just sufficient to curve the geometry up into closure, via its “effective” content of mass energy, both kinetic and potential. A parameter m' of time asymmetry in the Taub family of models allows one to adjust the ratio kinetic/potential at the phase of time asymmetry. A sufficiently extreme value of this parameter, m' = 10 12 , gives a universe that will live as long as a typical Friedmann “dust-dominated” model (“stay”) = 60 × 19 9 years, but will have a volume-at-maximum expansion smaller by a factor of 4.8 × 10 10 , or a (“beam”) = [(π/2) (volume at maximum)] 1/3 that is smaller than that of the Friedmann model by a factor of 3.64 × 10 3 . If with a universe so small it is nevertheless possible to secure a stretch of time quite adequate for the development of life, it is not clear what is the point of a larger universe. Neither is it clear how the anthropic principle of Dicke and Carter is to come to terms with this “missed chance for economy.”



Book ChapterDOI
01 Jan 1980
TL;DR: In this article, the density of the universe has been studied in the context of the distribution of galaxies in space and on intergalactic material, and the density is one of the four fundamental parameters observable within a gigaparsec and contributing to cosmology.
Abstract: Having collected all the available information on the distribution of galaxies in space and on intergalactic material, we are able to attack the problem of the density of the universe. This density is one of the four fundamental parameters observable within a gigaparsec and contributing to cosmology. The other three are the distance scale, the Hubble constant which we have already studied, and the age of the universe which is the subject of the next chapter.

Journal ArticleDOI
TL;DR: The contribution of the inhomogeneous universe to perihelion displacement is calculated in this paper, where the contribution of a single point in the universe to the periheroid displacement is analyzed.

Journal ArticleDOI
TL;DR: In this paper, it was shown that cosmic radiation almost follows a Planck distribution, because just as matter is formed, its density of energy is negligible in comparison with that of radiation, and that the present age of the universe does not depend on the particular manner in which the matter was formed.
Abstract: It is shown that cosmic radiation almost follows a Planck distribution, because just as matter is formed, its density of energy is negligible in comparison with that of radiation, and that the present age of the Universe does not depend on the particular manner in which the matter is formed.