The problem of the maximum volumes and particle horizon in the Friedmann universe model

The maximum volume of the closed Friedmann universe is further investigated and is shown to be 2² R ³ (t), instead of ² R ³ (t) as found previously. This discrepancy comes from the incomplete use of the volume formula of 3-dimensional spherical space in the astronomical literature. Mathematically, there exists the maximum volume at any cosmic timet in a 3-dimensional spherical case. However, the Friedmann closed universe in expansion reaches its maximum volume only at the timet _m of the maximum scale factorR(t _m ). The particle horizon has no limitation for the farthest objects in the closed Friedmann universe if the proper distance of objects is compared with the particle horizon as it should be. It will lead to absurdity if the luminosity distance of objects is compared with the proper distance of the particle horizon.     

Early Cosmological Models with Bulk Viscosity in Brans-Dicke Theory

The effect of time dependent bulk viscosity on the evolution of Friedmann models with zero curvature in Brans-Dicke theory is studied. The solutions of the field equations with ‘gamma-law’ equation of state p = (γ-1) ρ, where γ varies continuously as the Universe expands, are obtained by using the power-law relation φ = bR ⁿ , which lead to models with constant deceleration parameter. We obtain solutions for the inflationary period and radiation dominated era of the universe. The physical properties of cosmological solutions are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Possible Mechanism to Form Low Mass Objects at Low Redshifts

We develop a quantitative criterion for the collapse of matter within a region where a global texture just collapsed and a non-zero peculiar velocity field is produced. We also describe the evolution of the density contrast in this region according to the non-linear spherical collapse model. In particular, we find that the overdensity needed to virialisation is reached at z ≤ 2.2, covering a mass range of about 10⁴–10⁷ M_⊙ in the context of an Einstein-de Sitter universe.     

Main stages of evolution of matter in the universe. II

A possible scenario for the evolution of the universe following the big bang at t > 10^-5 sec is considered. The necessary conditions that must be present for the formation of stars and stellar systems to be possible are formulated. As a condition for the formation of stars we take kT_s≤ GM_sm_p(3R), and for stellar systems HR ? (GM/R)^1/2, where T_s is the temperature of the cosmic plasma, m_p is the mass of a proton, M_s is the mass of a star, M is the mass of a stellar cluster, R is the radius of these celestial bodies, and H is the bubble parameter for the corresponding time. In accordance with these criteria, we assume that in the course of cosmological expansion, neutron stars should have been formed first (times 2.10^-4 ? t ? 1 sec, densities 0.07 ? ρ_B? 2.10⁴ g/cm³) and then, in chronological order, appeared white dwarfs (t ≈ 10² sec, ρ_B ? 5.10^-3 g/cm³), ordinary stars (t ≈ 4.10⁶ sec, ?_B ≈ 10^-11 g/cm³), galactic nuclei (t ≈ 3.10¹¹ sec, ?_B ≈ 5.10^-19 g/cm³, globular clusters (t ≈ 10¹³ sec, ?_B ≈ 4.10^-21 g/cm³), and galaxies (t ≈ 10¹⁵ sec, ?_B ≈ 10^-24 g/cm³), where ?_B is the average density of ordinary (baryon) matter in the universe. It is shown that a galactic nucleus is a stellar system in statistical equilibrium and consists mainly of neutron stars and white dwarfs. The formation of some pulsars (neutron stars with angular rotation rates 1 < Ω < 200 sec^-1) may occur in a galactic nucleus. Observed pulsars should therefore contain some fraction of neutron stars from the nucleus of the Galaxy that were able to escape it over the relaxation time (the tail of the Maxwell distribution, with star velocities v > v₀, where v₀ is the velocity corresponding to the work function 2GMM_s/R, M being the mass and R the radius of the Galaxy’s nucleus.     

A finite temperature λφ4 model and A De Sitter — Friedmann transition in the early universe

We have analysed the finite temperature λφ⁴ model in the Robertson Walker metric, taking into consideration spontaneous symmetry breaking, particle production and symmetry recovery through phase transition under a high temperature, and found that it is possible to have a cosmological model free of singularities. Such a model begins in the singularity-free, horizon-free, Beltrami-Anti-de Sitter state. Continual production of particles keeps on raising its temperature until a critical temperature T_C is reached, when a phase change takes place, and the universe is transformed into a radiation-dominated, thermally-expanding Friedmann state. This phase transition corresponds to a big-bang without, however, an antecedent singularity.     

The massive scalar field in a closed Friedmann universe model — new rigorous results

For the minimally coupled scalar field in Einstein's theory of gravitation we look for the space of solutions within the class of closed Friedmann universe models. We prove D ≥ 1, where D ≥ is the dimension of the set of solutions which can be integrated up to t → ∞ (D > 0 was conjectured by PAGE (1984)). We discuss concepts like “the probability of the appearance of a sufficiently long inflationary phase” and argue that it is primarily a probability measure μ in the space V of solutions (and not in the space of initial conditions) which has to be applied. μ is naturally defined for Bianchi-type I cosmological models because V is a compact cube. The problems with the closed Friedmann model (which led to controversial claims in the literature) will be shown to originate from the fact that V has a complicated non-compact non-Hausdorff Geroch topology: no natural definition of μ can be given. We conclude: the present state of our universe can be explained by models of the type discussed, but thereby the anthropic principle cannot be fully circumvented.     

The cosmic age crisis and the Hubble constant in a non-expanding universe

The present paper outlines a cosmological paradigm based upon Dirac’s large number hypothesis and continual creation of matter in a closed static (nonexpanding) universe. The cosmological redshift is caused by the tired-light phenomenon originally proposed by Zwicky. It is shown that the tired-light cosmology together with continual matter creation has a universal Hubble constant H ₀=(512π ²/3)^1/6(GC ₀)^1/3 fixed by the universal rate C ₀ of matter creation, where G is Newton’s gravitational constant. It is also shown that a closed static universe has a finite age τ ₀=(243π ⁵/8GC ₀)^1/3 also fixed by the universal rate of matter creation. The invariant relationship H ₀ τ ₀=3π ²6^1/2 shows that a closed static universe is much older (≈one trillion years) than any expanding universe model based upon Big-Bang cosmology. It is this property of a static universe that resolves any cosmic age crisis provided that galaxy formation in the universe is a continual recurring process. Application of Dirac’s large number hypothesis gives a matter creation rate C ₀=4.6×10^?48 gm?cm^?3?s^?1 depending only on the fundamental constants of nature. Hence, the model shows that a closed static universe has a Hubble constant H ₀=70 km?s^?1?Mpc^?1 in good agreement with recent astronomical determinations of H ₀. By using the above numerical value for H ₀ together with observational data for elongated cellular-wall structures containing superclusters of galaxies, it is shown that the elongated cellular-wall configurations observed in the real universe are at least one hundred billion years old. Application of the microscopic laws of physics to the large-scale macroscopic universe leads to a static eternal cosmos endowed with a matter-antimatter symmetry. It is proposed that the matter-antimatter asymmetry is continuously created by particle-antiparticle pair annihilation occurring in episodic cosmological gamma-ray bursts observed in the real universe.     

Why is the universe homogeneous?

The very early universe must have been extremely homogeneous, even on scales far exceeding the particle horizon. Within the framework of the standard Friedmann cosmology, homogenization can only be achieved by quantum effects which violate classical causality. This could happen when the particle horizon was smaller than the Compton wavelength of the pion. The assumption that statistical departures from equilibrium started to grow after this epoch leads to a prediction of the density fluctuations at recombination. The amplitude ν of the fluctuations should have a maximum of about 0.007 on scales of 8₁₀17M. For smaller scales, ν ∝M ^+1/6, and for larger scales, ν ∝M ^?1/2. This suggests that superclusters condense out at a red shift of about 11, and clusters and then galaxies form shortly after by fragmentation.     

The influence of strong interactions on the early stages of the Universe

It is shown that the singularity of space-time in Einstein-Friedmann's cosmology can be avoided, if one takes into account the strong interaction of the elementary particles in the earliest stage of the Universe. Under the additional assumption that there exists a maximum temperature of particles and radiation (T _max?1.9×10¹² K) in consequence of which the number of hadrons (nucleons) in the early Universe has been greater than today by a factor of about 10⁷, the Friedmann equation is integrated numerically where the integration constant is fitted by the present values of the massdensity, the Hubble-constant and the temperature of the background radiation. The minimum radius of curvature of the Universe becomes 1.4×10¹¹ km; the density in its neighbourhood remains within reasonable limits of the magnitude of the nuclear density. The early evolution of the Universe with time will be discussed in detail. Concerning the idea of an universal upper limit for the temperature we follow the considerations of Hagedorn, but in contrast to the existing investigations we take explicitly into account the negative potential energy of the strong interaction according to Yukawa's theory.     

The large-scale structure of the universe in skewed cold dark matter models

We present results from N-body simulations of the clustering properties of the universe in a cubic box of size 260h⁻¹ Mpc, within a cold dark matter (CDM) cosmology with skewed distributions for initial adiabatic density perturbations δ_M. We consider two non-Gaussian models, Chi-squared and Lognormal, where the primordial gravitational potential is obtained from a non-linear transformation on a Gaussian random field. Our procedure yields for each model two primordial density distributions with opposite skewness δ³_M. The gravitational evolution and the present statistical properties of our simulations are strongly sensitive to the sign of the initial skewness. Skew-positive simulations produce a highly lumpy distribution with little power on large scales. Skew-negative simulations, on the contrary, evolve towards a cellular structure with high power on large scales, showing, in many respects, better agreement with observations than the standard CDM model. Giving up the random-phase hypothesis for primordial perturbations seems then a viable possibility to reproduce the large-scale properties of the universe; such a possibility is further motivated by many physical models either within the inflationary dynamics or phase transitions in the early universe.     

A case for the standard model

The fundamental properties of Friedmann Universes, which are attractive because of their simplicity, are linear expansion (except for deceleration), cooling, and evolution. In addition it is assumed that the fundamental constants of physics are constant and that the known laws of physics apply (including GR). An increasing number of observational tests support these premises. In particular the expansion is as linear as can be tested. The present expansion rate (H ₀ = 55 ± 10 km s^-1 Mpc^-1) implies an expansion age of 17.8 ± 3.2 Gyr (forq ₀ = 0) to 11.9 ± 2.1 Gyr (for q₀ = 1/2). This agrees perfectly within the errors, even for a critical Universe, with present age determinations of the oldest objects in the Galaxy which require 13.5 ± 2 Gyr.     

Seeable universe and its accelerated expansion: an observational test

From the equivalence principle, one gets the strength of the gravitational effect of a mass M on the metric at position r from it. It is proportional to the dimensionless parameter β ²=2GM/rc ², which normally is ?1. Here G is the gravitational constant, M the mass of the gravitating body, r the position of the metric from the gravitating body and c the speed of light. The seeable universe is the sphere, with center at the observer, having a size such that it shall contain all light emitted within it. For this to occur one can impose that the gravitational effect on the velocity of light at r is zero for the radial component, and non zero for the tangential one. Light is then trapped. The condition is given by the equality R _g =2GM/c ², where R _g represents the radius of the seeable universe. It is the gravitational radius of the mass M. The result has been presented elsewhere as the condition for the universe to be treated as a black hole. According to present observations, for the case of our universe taken as flat (k=0), and the equation of state as p=?ρc ², we prove here from the Einstein’s cosmological equations that the universe is expanding in an accelerated way as t ², a constant acceleration as has been observed. This implies that the gravitational radius of the universe (at the event horizon) expands as t ². Taking c as constant, observing the galaxies deep in space this means deep in time as ct, linear. Then, far away galaxies from the observer that we see today will disappear in time as they get out of the distance ct that is <R _g . The accelerated expanding vacuum will drag them out of sight. This may be a valid test for the present ideas in cosmology. Previous calculations are here halved by our results.     

Observational constraints on G-corrected holographic dark energy using a Markov chain Monte Carlo method

We constrain holographic dark energy (HDE) with time varying gravitational coupling constant in the framework of the modified Friedmann equations using cosmological data from type Ia supernovae, baryon acoustic oscillations, cosmic microwave background radiation and X-ray gas mass fraction. Applying a Markov Chain Monte Carlo (MCMC) simulation, we obtain the best fit values of the model and cosmological parameters within 1σ confidence level (CL) in a flat universe as: $\varOmega_{b}h^{2}=0.0222^{+0.0018}_{-0.0013}$ , $\varOmega_{c}h^{2}=0.1121^{+0.0110}_{-0.0079}$ , $\alpha_{G}\equiv \dot{G}/(HG) =0.1647^{+0.3547}_{-0.2971}$ and the HDE constant $c=0.9322^{+0.4569}_{-0.5447}$ . Using the best fit values, the equation of state of the dark component at the present time w _d0 at 1σ CL can cross the phantom boundary w=?1.     

Equilibrium Structures of Differentially Rotating Primary Components of Binary Stars

In this paper a method is proposed for computing the equilibrium structures and various other observable physical parameters of the primary components of stars in binary systems assuming that the primary is more massive than the secondary and is rotating differentially about its axis. Kippenhahn and Thomas averaging approach (1970) is used in a manner earlier used by Mohan, Saxena and Agarwal (1990) to incorporate the rotational and tidal effects in the equations of stellar structure. Explicit expressions for the distortional terms appearing in the stellar structure equations have been obtained by assuming a general law of differential rotation of the typeω² = b ₀+b ₁ s ²+b ₂ s ⁴, where ω is the angular velocity of rotation of a fluid element in the star at a distance s from the axis of rotation, and b ₀, b ₁, b ₂ are suitably chosen numerical constants. The expressions incorporate the effects of differential rotation and tidal distortions up to second order terms. The use of the proposed method has been illustrated by applying it to obtain the structures and observable parameters of certain differentially rotating primary components of the binary stars assuming the primary components to have polytropic structures. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dark matter-systematics of its distribution

The dynamical masses of dwarf-spheroidals, spiral and elliptical galaxies, dwarf irregular binaries, groups of galaxies and clusters are shown to lie in a band about the M ∼ ρR³ line. The value of ρ is approximately the same as that estimated for unseen matter in the solar neighbourhood. The clusters themselves lie about theM ∼ R ^-3 line derived for a self-gravitating neutrino gas; their masses are distributed around the maximum Jeans-mass, M_Jmax. corresponding to m_v - 10 eV in an expanding universe. The present day length scales of clusters and the dispersion in the velocities observed within them are understood in terms of a 100-fold expansion subsequent to the initial growth of the fluctuations at M_Jmax. These systematics on theR-M plane imply that the initial condensations in the expanding universe are on the scale of the rich clusters of galaxies, these condensations were triggered dominantly by the gravitation of the neutrinos and the constant density of al systems arises naturally due to the embedding of these systems in the large scale neutrino condensations. If the neutrino density falls off asr ^-2 beyond the cluster edge till the distributions from different clusters overlap, then the mean density of the neutrinos approximately equals the closure density of the universe.     

The Global Structure of the Colliding Bubble Braneworld Universe

The one-brane Randall-Sundrum model offers an example of a model with an `infinite' extra dimension in which ordinary gravity is recovered at large distances and the usual (3+1)-dimensional cosmology at late cosmic times. This is possible because the `bulk' has the geometry of anti de Sitter space, the curvature length ℓ of which delineates the (3+1)-dimensional behavior at large distances from the (4+1)-dimensional behavior at short distances. This spacetime, however, possesses a past Cauchy horizon on which initial data must be specified in a natural and convincing way. A more complete story is required that singles out some set of initial conditions to resolve the `bulk' smoothness and horizon problems. One such complete story is offered by the colliding bubble braneworld universe, where bubbles filled with AdS ⁵ nucleate from dS ⁵ or M ⁵ through quantum tunnelling. A pair of such colliding bubbles forms a Randall-Sundrum-like universe in the future of the collision. Because of the symmetry of bubbles produced through quantum tunnelling, the resulting universe is spatially homogeneous and isotropic at leading order, and the perturbations at the next order are completely well defined and calculable. In this contribution we discuss the possible global structure of such a spacetime. This revised version was published online in July 2006 with corrections to the Cover Date.     

Radar and photoelectric observations of asteroid 2100 Ra-Shalom

Results of 13-cm-wavelength radar observations and V-filter photoelectric observations of Ra- Shalom during its 1981 Aug–Sep apparition are reported. The radar data yid detections of echoes in the same sense of circular polarization as transmitted (i.e., the SC sense) as well as in the opposite (OC) sense. The estimate of the ratio of SC to OC echo power, μ_c = 0.14 ± 0.02, indicates that most, but certainly not all, of the backscattering is due to single reflections from surface elements that are fairly smooth at decimeter scales. The value obtained for the OC radar cross section on Aug 26 (1.2 ± 0.3 km²) is about three times larger than those obtained on Aug 23, 24, and 25. The echo bandwidth appears to be within about 1.5 Hz of 5.0 Hz on each date. The photoelectric data suggest a value, P_syn = 19.79 hr, for the synodic rotation period, and yield a composite lightcurve with two pairs of extrema. Combining this value for P_syn with a firm lower bound (4 Hz) on the maximum echo bandwidth yields a lower bound of 1.4 km on the maximum distance between Ra-Shalom's spin axis and any point on its surface.     

Search for Cometary Activity in KBO (24952) 1997 QJ4

Deep imaging was performed with the Subaru Telescope on Mauna Keacentered on the position of the KBO (24952) 1997 QJ₄ on 2half-nights during October 2002. A deep search for evidence of a dustcoma was conducted which could be indicative of cometary activity downto a limit of m_V = 31 mag arcsec^-2. No coma was detected, and from this sensitive upper limits on dust production can be set at Q <0.01 kg s^-1. Brightness variations consistent with rotationalmodulation were seen, implying a period of rotation longer than 4 hrs,with a range > 0.3 mag corresponding to a minimum projected axis ratioof 1:1.3.     

Structurally stable approximations to Friedmann—Lemaître world models

Friedmann—Lemaître cosmology is briefly reviewed in terms of dynamical systems. It is demonstrated that in certain cases bulk viscosity dissipation structurally stabilizes Friedmann—Lemaître solutions. It turns out that, for A=0, there are structurally stable solutions if ξ~ε^1/2, where ξ is the bulk viscosity coefficient. For A≠0 structurally stable solutions are essentially those with ξ=const. The role of structural stability in physics and cosmology is shortly discussed.     

Oscillating Universe – An Alternative Approach in Cosmology

A new paradigm in cosmology is presented: A geometrical phase transition from the Minkowski space to an anti-deSitter space at its maximum of extension instead of a big bang with inflation. This scenario implies an open universe with a negative cosmological constant which replaces completely the cold dark matter in galaxy clusters. Baryonic matter and radiation are created from the gravitational field over a very long period of about 30 billion years. The contracting universe runs then after a further period of 13 billion years through a minimum with T _max ≃ 1.8 × 10¹² K and a particle density n _max ≃ 5 × 10³⁸ cm^-3 due to Hagedorn’s theory of a hadron gas. After the run through the minimum the universe expands like a big bang universe and reaches due to the negative cosmological constant after 44 billion years its maximal extension. Then it contracts again, and so on: An open ever-oscillating universe.