Gravitational clustering of galaxies in an expanding universe

We inquire the phenomena of clustering of galaxies in an expanding universe from a theoretical point of view on the basis of thermodynamics and correlation functions. The partial differential equation is developed both for the point mass and extended mass structures of a two-point correlation function by using thermodynamic equations in combination with the equation of state taking gravitational interaction between particles into consideration. The unique solution physically satisfies a set of boundary conditions for correlated systems and provides a new insight into the gravitational clustering problem.     

Solving the graceful exit problem in superstring cosmology

We briefly review the status of the “graceful exit” problem in superstring cosmology and present a possible resolution. It is shown that there exists a solution to this problem in two-dimensional dilaton gravity provided quantum corrections are incorporated. This is similar to the recently proposed solution of Rey. However, unlike in his case, in our one-loop corrected model the graceful exit problem is solved for any finite number of massless scalar matter fields present in the theory.     

Concerning the instantaneous mass and the extent of an expanding universe

In this article we want to answer the cosmologically relevant question what, with some good semantic and physical reason, could be called the massM _u of an infinitely extended, homogeneously matter‐filled and expanding universe. To answer this question we produce a space‐like sum of instantaneous cosmic energy depositions surrounding equally each spacepoint in the homogeneous universe. We calculate the added‐up instantaneous cosmic energy per volume around an arbitrary space point in the expanding universe. To carry out this sum we use as basic metrics an analogy to the inner Schwarzschild metric applied to stars, but this time applied to the spacepoint‐related universe. It is then shown that this leads to the added‐up proper energy within a sphere of a finite outer critical radius defining the point‐related infinity. As a surprise this radius turns out to be reciprocal to the square root of the prevailing average cosmic energy density. The equivalent mass of the universe can then also be calculated and, by the expression which is obtained here, shows a scaling with this critical radius of this universe, a virtue of the universe which was already often called for in earlier works by E. Mach, H. Thirring and F. Hoyle and others. This radius on the other hand can be shown to be nearly equal to the Schwarzschild radius of the so‐defined mass M _u of the universe. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Field theory of the correlation function of mass density fluctuations for self-gravitating systems

The mass density distribution of Newtonian self-gravitating systems is studied analytically in the field theoretical method. Modeling the system as a fluid in hydrostatic equilibrium, we apply Schwinger's functional derivative on the average of the field equation of mass density, and obtain the field equation of 2-point correlation function ξ(r) of the mass density fluctuation, which includes the next order of nonlinearity beyond the Gaussian approximation. The 3-point correlation occurs hierarchically in the equation,and is cut off by the Groth-Peebles ansatz, making it closed. We perform renormalization and write the equation with three nonlinear coefficients. The equation tells us that ξ depends on the point mass m and the Jeans wavelength scale λ_0, which are different for galaxies and clusters. Applying this to large scale structures, it predicts that the profile of ξcc for clusters is similar to ξgg for galaxies but with a higher amplitude, and that the correlation length increases with the mean separation between clusters, i.e., a scaling behavior r_0■0.4 d. The solution yields the galaxy correlation ξ_gg(r)■(r_0/r)^1.7 valid only in a range1 < r < 10 h^-1 Mpc. At larger scales the solution ξgg deviates below the power law and goes to zero around ~50 h^-1 Mpc, just as the observations show. We also derive the field equation of the 3-point correlation function in the Gaussian approximation and its analytical solution, for which the Groth-Peebles ansatz with Q = 1 holds.     

Quantization of the Bianchi type universe

In this paper, we have used a square root formulation of the Wheeler-De Witt equation to quantize a minisuperspace model consisting of the Bianchi-I type universe with a radiation field source. We have derived a wavefunction with a conserved current and a positive-definite probability density.

We have also explored the third quantization of the Bianchi type universe using a procedure usual in the quantum field theory of curved space-time. We have given the wave function that satisfies the Wheeler-De Witt equation. By regarding the wave function as the universe field operator in a minisuperspace, we have not only circumvented the difficulty of a probabilistic interpretation in quantum cosmology, we have also reached the conclusion that multiple universes would result. We have estimated the average number of universes produced from ‘nothing’, and have given their distribution, which turned out to be a Planck distribution.     

The maximal photon mean free path sphere and the observable universe

The objective of this paper is to draw attention to the close similarity between the observable universe and the photon mean free path sphere. It is hoped that by analyzing in depth this apparent connection one will be able to explain why our present epoch appears to have special properties. It is shown that some theoretical arguments point to an equality between the number of particles in the observable universe and the number of particles in the largest self-gravitating photon mean free path sphere (MxPhMFPS.) This equality, supported by observational data, leads to a series of equations that relate in simple manner characteristics of the observable universe with characteristics of the MxPhMFPS, and allows a more precise approximation of the values of the main cosmological parameters. It is also shown that by replacing the protons in the MxPhMFPS with positrons, the radiation resulted by their interaction with the existing electrons has an energy equal to the energy of the electromagnetic radiation in the observable universe.     

Absence of initial singularities in superstring cosmology

In a universe whose elementary constituents are point particles there does not seem to be any obvious mechanism for avoiding the initial singularities in physical quantities in the standard model of cosmology. In contrast in string theory these singularities can be absent even at the level where spacetime is treated classically. This is a consequence of the basic degrees of freedom of strings in compact spaces, which necessitate a reinterpretation of what one means by a very small universe. We discuss the basic degrees of freedom of a string at the classical and quantum level, the minimum size of strings (string uncertainty principle), the t-duality symmetry, and string thermodynamics at high energy densities, and then describe how these considerations suggest a resolution of the initial singularity problem. An effort has been made to keep this writeup self-contained and accessible to non-string theorists.     

Is the universe homogeneous? (On large scales)

I critically discuss in a pedagogical and phenomenological way a few crucial tests challenging the recent claims by Pietronero and collaborators that there is no evidence from available galaxy catalogues that the Universe is actually homogeneous above a certain scale. In a series of papers, these authors assert that observations are consistent with a fractal distribution of objects extending to the limit of the present data. I show that while galaxies are indeed clustered in a scale-free (fractal) way on small and intermediate scales, this behaviour does not continue indefinitely. Although the specific wavelength at which the galaxy distribution apparently turns to homogeneity is dangerously close to the size of the largest samples presently available, there are serious hints suggesting that this turnover is real and that its effects are detected in the behaviour of statistical estimators. The most recent claims of a continuing fractal hierarchy up to scales of several hundreds Megaparsecs seem to be ascribable to the use of incomplete samples or to an improper treatment of otherwise high-quality data sets. The fractal perspective, nevertheless, represents a fruitful way to look at the clustering properties of galaxies, when properly coupled to the traditional gravitational instability scenario. In the last part of this paper I will try to clarify, at a very simple level, some of the confusion existing on the actual scaling properties of the galaxy distribution, and discuss how these can provide hints on the evolution of the large-scale structure of the Universe.     

Effect of modified Chaplygin gas in anisotropic universe

In this work, we have studied the model of modified Chaplygin gas and its role in accelerating phase of the universe for anisotropic model. We have assumed that the equation of state of this modified model is valid from the radiation era to ΛCDM model. We have obtained the possible relation between the hessence and the modified Chaplygin gas. We have also use the statefinder parameters for characterize different phase of the universe diagrammatically.     

超弦理论中的宇宙波函数

本文讨论了超弦理论中的宇宙波函数，使用Ｖｉｌｅｎｋｉｎ的边界条件，我们得到了膨胀子场Ｄ的值给定时宇宙标度因子ａ的几率分布。我们还得到了宇宙自发成核时，经典宇宙的标度因子的最小值为Ｐｌａｎｃｋ长度的数量级，这说明量子效应能阻止宇宙塌缩到奇点。     

Abell-ACO团二维分布中的结构

本文用团分析法分别对距离类D＝5及D＝6的Abell－ACO团的二维分布进行了分析．分析的目的是探讨星系团分布中可能存在的超大尺度结构．分析结果表明：富星系团分布中的确存在尺度≥100h-1Mpc的超大尺度结构．本文的分析为超大尺度结构的存在提供了又一支持．     

Evolution of the luminosity function and colours of galaxies in a Λ cold dark matter universe

The luminosity function of galaxies is derived from a cosmological hydrodynamic simulation of a Λ cold dark matter universe with the aid of a stellar population synthesis model. At     , the resulting B -band luminosity function has a flat faint-end slope of     with the characteristic luminosity and the normalization in fair agreement with observations, while the dark matter halo mass function is steep with a slope of     . The colour distribution of galaxies also agrees well with local observations. We also discuss the evolution of the luminosity function, and the colour distribution of galaxies from     to 5. A large evolution of the characteristic mass in the stellar mass function as a result of number evolution is compensated by luminosity evolution; the characteristic luminosity increases only by 0.8 mag from     to 2, and then declines towards higher redshift, while the B -band luminosity density continues to increase from     to 5 (but only slowly at     .     

Kinetic and chemical equilibrium of the Universe and gravitino production

Flat directions in generic supersymmetric theories can change the thermal history of the Universe. A novel scenario was proposed earlier where the vacuum expectation value of the flat directions induces large masses for all the gauge bosons and gauginos. This delays the thermalization of the Universe after inflation and solves the gravitino problem. In this article we perform a detailed calculation of the above scenario. We include the appropriate initial state particle distribution functions, consider the conditions for the feasibility of the non-thermal scenario, and investigate phase space suppression of gravitino production in the context of heavy gauge bosons and gauginos in the final state. We find that the total gravitino abundance generated is consistent with cosmological constraints.     

Kinetic Alfvén wave driven by the density inhomogeneity in the presence of loss-cone distribution function—particle aspect analysis

Kinetic Alfven waves (KAWs) driven by the diamagnetic drift instability that is excited by the density inhomogeneity in low-β plasmas, such as plasmas in the auroral region, are investigated by adopting the particle aspect analysis and loss-cone distribution function. The results obtained in this paper indicate that the propagation and evolution of kinetic Alfven waves decrease and the kinetic Alfven wave excitation becomes not easier with increasing loss-cone index J. But the spatial scales of the perpendicular perturbation driving kinetic Alfven waves have a decreasing tendency with the larger values of J, which perhaps is in relation with the decreasing width of loss-cone. A single hump appears in the plots of the growth rate of the instability when J=2. But the hump cannot emerge when J=0 or J=1. The density inhomogeneity of ions plays an important role in driving KAWs and it cannot be ignored. KAWs can be easier driven and KAWs can propagate and evolve faster with the increasing level of density inhomogeneity. However, the range of the perpendicular wave number of the wave instability decreases, namely, the longer the scale of perpendicular disturbance the easier the excitation of KAW. As the density inhomogeneity increases, the tendency of numerical solutions of the dispersion relation is similar to that obtained by the kinetic theory and Maxwellian distribution function (Duan and Li, 2004). But the profiles of the plots of numerical solutions are different. This means that the velocity distribution function of particles is important for KAW driven in magnetoplasmas, especially in the active regions of the magnetosphere, such as auroral region, and plasma sheet boundary.     

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.     

Effect of dynamical cosmological constant in presence of modified Chaplygin gas for accelerating universe

In this paper we have considered the Universe to be filled with Modified Gas and the Cosmological Constant Λ to be time-dependent with or without the Gravitational Constant G to be time-dependent. We have considered various phenomenological models for Λ, viz., and . Using these models it is possible to show the accelerated expansion of the Universe at the present epoch. Also we have shown the natures of G and Λ over the total age of the Universe. Using the statefinder parameters we have shown the diagrammatical representation of the evolution of the Universe starting from radiation era to ΛCDM model.     

The effect of cosmological background dynamics on the spherical collapse in MOND

The effect of background dynamics of the universe on formation of large scale structures in the framework of Modified Newtonian Dynamics (MOND) is investigated. A spherical collapse model is used for modeling the formation of the structures. This study is done in two extreme cases: (i) assuming a universe with a low-density baryonic matter without any cold dark matter and dark energy; (ii) a dark energy dominated universe with baryonic matter, without cold dark matter. We show that for the case (ii) the structures virialize at lower redshifts with larger radii compared to the low-density background universe. The dark energy slow downs the collapse of the structures. We show that our results are compatible with recent simulations of the structure formation in MOND.     

Phenomenological models of cosmic phase transitions II. Application of the classical nucleation theory

Classical nucleation theory is applied to follow the thermal history of a homogeneous and isotropic universe during a first-order phase transition. The dependence of possible supercooling and reheating scenarios on the surface tension and growth velocity of bubbles is discussed.     

Structure in the two-dimensional distribution of Abell-ACO clusters

We study the structure in the two-dimensional distribution of Abell-ACO clusters of distance classes D = 5 and D = 6, using cluster analysis. The results show that there are real structures on scales ≥ 100h⁻¹ Mpc, thus providing additional evidence for the existence of structure on the super-large scale.