Relativistic hierarchical cosmology

While Euclidean models with uniform matter density have a number of radio sources of flux density greater thanF at frequencyv that varies asN(>F, v)¹ F ^–3/2, hierarchical models with = ₀ r ^–2 haveN(>F,)F ^–1/2 (Section 1). Since the observed dependency isN(>F,)F ^–1.8, severe density and/or luminosity evolution must be present in a workable hierarchical cosmology (Section 2). The same argument applies (Section 3) to the number of sources of apparent luminosity greater thanl,N(>l) and (Section 4) to the number of sources within redshift distancez from the local origin. To give agreement with empirical data demandsq _o=+1 and large first and second derivatives with respect to time of the number source density (Section 5). The adoption ofq _o=+1 allows one to show (Section 6) that a Lemaitre-type hierarchical Universe with a long coasting or waiting time can give agreement with observations of the numbers of QSO's etc. if the age of the Universe is more than 10¹³ yr. The dependence of the effective Hubble parameter onk(t), (t) andR (Section 7) leads one to suggest that ak=0, =0 hierarchy with 0 might be the simplest acceptable form of model Universe. Section 8 (Conclusion) points out that further data on source count anisotropies should allow the component levels of the hierarchy to be delineated.     

On hierarchical cosmology

Progress in laboratory studies of plasmas and in the methods of transferring the results to cosmic conditions, together within situ measurements in the magnetospheres, are now causing a ‘paradigm transition’ in cosmic plasma physics. This involves an introduction ofinhomogeneous models with double layers, filaments, ‘cell walls’, etc. Independently, it has been discovered that the mass distribution in the universe is highly inhomogeneous; indeed,hierarchical. According to de Vaucouleurs, the escape velocity of cosmic structures is 10²–10³ times below the Laplace-Schwarzschild limit, leaving avoid region which is identified as a key problem in cosmology. It is shown that a plasma instability in the dispersed medium of the structures may produce this void and, hence, explain the hierarchical structure. The energy which is necessary may derive either from gravitation or from annihilation caused by a breakdown of cell walls. The latter alternative is discussed in detail. It leads to a ‘Fireworks Model’ of the evolution of the metagalaxy. It is questioned whether the homogeneous four-dimensional big bang model can survive in an universe which is inhomogeneous and three-dimensional.     

Relativistic hierarchical cosmology

In this paper we discuss a hierarchical model of Universe which was proposed by Wesson (1975). We assert that the mathematical formalism used by Wesson leads to contradiction with Einstein's equations.     

Symmetry in hierarchical cosmology

An idealized model of a hierarchy of clusters is considered, and the number-count asymmetry measure in two different directions,R ₁ |N ⁺-N ^-|/(N ⁺+N ^-), is evaluated, for values ofl _I /c _I =(distance between cluster centres)/(cluster diameter). Providedl _I /c _I 10, theory predictsR _I 0.1, in agreement with the symmetry of high-redshift radio sources.     

The continuing case for a hierarchical cosmology

The standard ‘Big Bang’ and hierarchical paradigms for describing the cosmos are discussed in terms of recent astrophysical discoveries. Three criteria established by G. de Vaucouleurs in 1970 as bases for deciding between these two cosmological models provide the main format of the discussion.     

Expanding and superdense astrophysical systems in general relativistic hierarchical cosmology

A semi-continuous hierarchy, (i.e., one in which there are galaxies outside clusters, clusters outside superclusters etc.), is examined using an expression of the field equations of general relativity in a form due to Podurets, Misner and Sharp. It is shown (a) that for a sufficiently populous hierarchy, the thinning factor( _i+1/ _i [r _i /r _i+1] is approximately equal to the exponentN in a continuous density law (=aR ^–N) provided (r _i /r _i+1)^3-1; (b) that a hierarchical Universe will not look decidedly asymmetric to an observer like a human being because such salient observers live close to the densest elements of the hierarchy (viz stars), the probability of the Universe looking spherically symmetric (dipole anisotropy0.1 to such an observer being of order unity; (c) the existence of a semi-continuous or continuous hierarchy (Peebles) requires that 2 if galaxies, not presently bound to clusters were once members of such systems; (d) there are now in existence no less than ten arguments for believing 2, though recent number counts by Sandageet al. seem to be in contradiction to such a value; (e) Hubble's law, withH independent of distance, can be proved approximately in a relativistic hierarchy provided (i)N=2, (ii)2GM(R)/c ² R1; (iii)Rc (iv)M0 in a system of massM, sizeR (f) Hubble's law holds also in a hierarchy with density jumps; (g)H100 km s^–1 Mpc^–1; (h) objects forming the stellar level of the hierarchy (in a cosmology of the Wilson type) must once have had 2GM/c ² R1; (i) there is a finite pressurep=2Ga in all astrophysical systems (a=R ^N ,N2); (j) for the Galaxy, theory predictsp _G7×10^–12 dyn cm^–2, observation givesp _G5×10^–12 dyn cm^–2; (k) if the mass-defect (or excess binding energy) hypothesis is taken as a postulate, all non-collapsed astrophysical systems must be non-static, and any non-static, p0 systems must in any case be losing mass; (1) the predicted mass-loss rate from the Sun is 10¹² g s^–1, compared to 10¹¹ g s^–1 in the observed solar wind; (m) the mass-loss rates known by observation imply timescales of 5×10⁹ years for the Sun and 10¹⁰ years for other astrophysical systems; (n) degenerate superdense objects composed of fermions must haveN-2 if they were ever at their Schwarzschild radii and comprised a finite numberN _B of baryons; (o)N _B10⁵⁷N for degenerate fermion and boson systems; (p)285-4; (q) the metric coefficients for superdense bodies give equations of motion that imply equal maximum luminosities for all evolving superdense bodies (L _max10⁵⁹ erg s^–1); (r) larger bodies have longer time-scales of energy radiation atL _max (10^–5 s for stars,1 h for QSO's) (s) expansion velocities are c soon after the initial loss of equilibrium in a superdense object; (t) if the density parametera(t) in aR ^–N isa=a (non-atomic constants of physicsc, G, A), andA, thenN=2; (u) N2 is necessary to giveMM at the stellar level of the hierarchy;(v) systems larger than, and including, galaxies must have formed by clumping of smaller systems and not (as advocated by Wertz and others) in a multiple big bang.     

Theoretical determination of the thinning factor in relativistic hierarchical cosmology

Recent computer simulations by Haggerty (1974) and Haggerty and Janin (1974) on the gravitational clumping of bodies into clusters and superclusters in Newtonian cosmology have given an approximate value of Θ=1.9 for the thinning factor (defined for two systems of sizesR ₁,R ₂ and densities? ₁,? ₂ by? ₁/? ₂ = (R ₂/R ₁)^θ), close to the observed value of Θ=1.7. To get an almost exact value of Θ in a general relativistic hierarchy, algebraic conditions on the metric tensor are employed: the result is Θ=2, with the hierarchy characterized by a dimensionless constantη ₁ (?G?b ²/c²) of valueη ₁ ? 2 x 10^-7 (?=density,b=characteristic dimension, of any system at any level of the hierarchy). A condition on the rotation of systems is also found for objects of sufficiently high angular momentum.     

Expanding clusters of galaxies as components of a relativistic hierarchical cosmology

Approximate metries for clusters embedded in an expanding Robertson/Walker background (Section 1) indicate that in general clusters of galaxies cannot remain uninfluenced by the expansion. The potential for an expanding cluster (Section 2) is seen to suggest that clusters as presently observed are not in static equilibrium and that the missing mass problem can be elucidated via use of the virial theorem (Section 3) given certain density conditions in compact clusters. Non-compact clusters can be treated similarly, and it is found that the behaviour of a low-density cluster is equivalent to that of a domain of a Friedmann (k=0) model Universe (Section 4). The treatment of compact clusters (Section 5) is based on approximate metrics for clusters embedded in a Robertson/Walker background. These comparisons lead to information on the evolution of non-compact clusters and compact clusters (Section 7), and to observable consequences that seem to be borne out successfully (Section 8). Data on clusters themselves tend to show that there exists an expanding supercluster and/ or that >0 (Section 9). Several tests of the hypothesis of expansion of clusters (Section 10) are proposed.     

An empirical approach to cosmology

A two-component model of the universe is proposed, based on the observations of discrete extragalactic sources and the microwave background radiation. The large scale dynamics of the universe is determined by the radiation component and it leads to a characteristic size of the universe 6×10⁵ Mpc and an age 10¹² yr. The second component, that of matter, occurs in discrete sources which group together in super-superclusters of characteristic size 6×10³ Mpc and age 10¹⁰ yr. It is suggested that our Galaxy belongs to one of these super-superclusters and that observations of discrete sources are confined to this unit. A reasonable agreement with the cosmological tests is obtained on the assumption that the geometry within a typical super-supercluster is Euclidean and that the redshifts of galaxies arise from Doppler effect due to motions originating in a local explosion which gave birth to the super-supercluster. Further observational checks on this model are proposed.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation     

Vacuum friedmann model in self-creation cosmology

The field equations of the self-creation theory of gravitation proposed by Barber are solved for a vacuum with the aid of a space-time metric of Friedmann. Some physical properties of the solution are discussed.     

An exact Bianchi type-V cosmological model in Saez-Ballester theory of gravitation

An exact Bianchi type-V cosmological model is obtained in a scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986) in case of perfect fluid distribution. Some physical properties of the model are also discussed.     

Discrete source counts and the rotation of the local Universe in hierarchical cosmology

Attention is given to four reasons for believing that the upper limit on the rotation of the Universe ω set by isotropy of the 3K background may not be appropriate to the local system because of its hierarchical structure. In particular, recent work of Rubinet al. (1973) on the anisotropy of Hubble's parameter (H) as determined by certain galaxies is examined. The anisotropy inH is a 1st order harmonic effect, inconsistent with an origin in an acceleration of the expansion of the Universe (U _α;4≠0), but explicable as being due to a large peculiar velocity of the Local Group. This compromises limits set on ω by isotropy of the 3K field, as does the realization that only weak limits can be set if the last-scattering surface (z _*) is notz _*→∞ but is at smallz _* (as expected in a hierarchy). In a rotating Universe, the 3-spaces of constant density cannot be orthogonal on the world lines of matter: a number test of Gödell based on this is generalized and applied (after consideration of Galactic obscuration) to the local Universe, by taking data on clusters of galaxies from the Abell and Zwicky catalogues. Data from the former give only a marginally significant result for the component ω₁ of ω in one direction, but a bootstrap argument is applied which takes significance over from Abell's data (considered as a class of galaxies) to Zwicky's data (taken as a class of clusters), giving a statistically significant result on the hypothesis that clusters are the fundamental units of the Universe: it seems likely that ω₁r?(const)r^-n with 0?n?1 over the interval 500–1000 Mpc (H=60 km s^?1 Mpc^?1) with a total rotation of ω<2ω₁, and ω₁ = 1.2 (+0.25) x 10^-18 s^-1 evaluated on data out to 10³ Mpc. Strictly, the quoted value of the rotation only applies to a region of space that in some sense has an isotropic limit: if the actual hierarchy has a large density-dependence away from a local origin (i.e., large thinning factor), then the numerical value of the rotation is smaller than the quoted value but still finite and significant.     

Some exact solutions of string cosmology with heat flux in Bianchi type III space-time

In this paper, the Einstein field equations have been solved for a cloud of string with heat flux in Bianchi type III space-time. The physical and geometrical properties of the model have been examined.     

Bianchi type-V radiating model in self-creation cosmology

The spatially-homogeneous and anisotropic cosmological model in self-creation theory of gravitation proposed by Barber, is obtained in the presence of perfect fluid with disordered radiation and the metric is of Bianchi type-V. Some physical properties of the model are discussed.     

A model cosmology based on gravity-electromagnetism unification

In this article the GEM (Brandenburg, 1992; Brandenburg, 1988) theory is applied to the problem of the cosmos in which most of the matter is hydrogen, spacetime is flat, and a Cosmic Background Radiation CBR field exists. Using the two postulates of the GEM theory: 1. That gravity fields are equivalent to an array ofE ×B drifts or a spacially varying Poynting field, such that spacetime is determined by EM fields so that the stress tensor of ultrastrong fields is self-canceling; 2. That EM and gravity fields and protons and electrons are unified at the Planck scale of lengths and energies and split apart to form distinct fields and separate particles at the Mesoscale of normal particle rest energies and classical radii. A new derivation is made of the formula forG found previously:G =e ²/(m _p m _e ) exp(-2R ^1/2) = 6.668 × 10^–8 dynes cm² g^–2wherem _p andm _e are the proton and electron masses respectively,R =m _p /m _e and is the fine structure constant, shows that quantum processes may occur which make the vacuum unstable to appearance of hydrogen thus allowing matter creation and a steady state universe to occur. The value for the Hubble Time calculated from this model isT _o = (3/((2)(R ^1/2)⁴))^1/3(r _e /c)(e ²/Gm _p m _e )= 19 Gyr wherer _e =e ² / (m _e c ²)and follows the form first hypothesized by Dirac(1937). The CBR is traced to this process of matter creation and its temperature is calculated as beingT _CBR = ((3/4)Gm _e ² c/( ² _o ))^1/4 = 2.66K where is the Thomson cross section of the electron and _o is the Stefan-Boltzman constant.     

Bianchi type-I vacuum model in self-creation cosmology

A simple and elegant generalisation of the Kasner model is presented in a self-creation theory of gravitation, proposed by Barber by solving the field equations corresponding to the Bianchi type-I metric. Some physical properties of the model are discussed.     

An alternative approach to cosmogony and cosmology

Some problems associated with the big bang cosmological model are briefly discussed. It is shown that the quasi-steady state model (QSSC) is a viable alternative. Moreover, the cosmogony related to this theory is supported by the observations.     

A static conformally-flat vacuum model in self-creation cosmology

Vacuum field equations for the conformally-flat spherically-symmetric static space-time are obtained in a self-creation theory of gravitation proposed by Barber. It is shown that the most general conformally-flat spherically-symmetric static vacuum model in this theory represents only purely flat space-time.     

Axially symmetric radiating cosmological model in a self-creation cosmology

An axially symmetric space time is considered in the presence of a perfect fluid source in Barbers (Gen. Relativ. Gravit. 14, 117, 1982) second self creation theory of gravitation. An exact radiating cosmological model is presented using a relation between the metric potentials. Some physical and kinematical properties of the model are also discussed.