Frozen Rigging Model of the Energy Dominated Universe

Composite rigging systems, involving membranes that meet on strings that meet on monopoles, arise naturally by the Kibble mechanism as topological defects in field theories involving spontaneous symmetry breaking. Such systems will tend to freeze out into static lattice type configurations with energy contribution ultimately be provided by the membranes. It has been suggested by Bucher and Spergel that on scales large compared with the relevant (interstellar separation) distance characterizing the relevant mesh length, such a system may behave as a rigidity-stabilized solid, having an approximately isotropic stress energy tensor with negative pressure, as given by a polytropic index γ = w+1 = 1/3. It has recently been shown that such a system can be rigid enough to be stable if the number of membranes meeting at a junction is even (though not if it is odd). Using as examples an approximaely O(3) symmetric scalar field model that can provide an “8-color” (body-centered) cubic lattice, and an approximate U(1)× U(1) model offering a disordered “5-color” lattice, it is argued that such a mechanism can account naturally for the observed dark energy dominance of the universe, without ad hoc assumptions, other than that the relevant symmetry breaking phase transition should have occurred somewhere about the Kev energy range.     

Gravitational fields with space-times of Bianchi type IX

Spatially homogeneous space-times of Bianchi type IX are considered. A general scheme for the derivation of exact solutions of Einstein’s equations corresponding to perfect fluid plus pure radiation fields is outlined. Some simple rotating Bianchi type IX cosmological models are presented. The details of these solutions are also discussed. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

On the accelerated expansion of the cosmos

We present a short (and necessarily incomplete) review of the evidence for the accelerated expansion of the Universe. The most direct probe of acceleration relies on the detailed study of supernovae (SN) of type Ia. Assuming that these are standardizable candles and that they fairly sample a homogeneous and isotropic Universe, the evidence for acceleration can be tested in a model-independent and calibration-independent way. Various light-curve fitting procedures have been proposed and tested. While several fitters give consistent results for the so-called Constitution set, they lead to inconsistent results for the recently released SDSS SN. Adopting the SALT fitter and relying on the Union set, cosmic acceleration is detected by a purely kinematic test at 7σ when spatial flatness is assumed and at 4σ without any assumption on the spatial geometry. A weak point of the described method is the local set of SN (at z<0.2), as these SN are essential to anchor the Hubble diagram. These SN are drawn from a volume much smaller than the Hubble volume and could be affected by local structure. Without the assumption of homogeneity, there is no evidence for acceleration, as the effects of acceleration are degenerate with the effects of inhomogeneities. Unless we sit in the centre of the Universe, such inhomogeneities can be constrained by SN observations by means of tests of the isotropy of the Hubble flow.     

A consistent numerical scheme for self‐gravitating fluid dynamics

In this article, we present a numerical scheme for the 3‐D system of self‐gravitating fluid dynamics in the collisional case as well as in the non‐collisional case. Consistency in the sense of distributions is proved in 1‐D and in absence of pressure. In the other cases consistency is proved under the numerical assumptions of boundedness of the velocity field in the CFL condition and of boundedness of the gradient of the gravitation potential. In 2‐D and 3‐D, concentrations of matter in strings and points can cause a theoretical difficulty in the pressureless case although one observes that the scheme still works. The initial data are L^∞ functions in velocity and L¹ functions in density. Applications are given to numerical simulations of the role of dark matter and gravitational collapse in cosmology as well as Jeans theory. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

Time‐reparametrization invariance and Hamilton‐Jacobi approach to the cosmological σ‐model

The construction of physical models with local time‐reparametrization invariance is reviewed. Negative‐energy contributions to the hamiltonian are shown to be crucial for the realization of this reparametrization symmetry. The covariant formulation of the dynamics is used to develop a time and gauge invariant Hamilton‐Jacobi theory. This formalism is applied to solve for the cosmology of a homogeneous universe of the Friedmann‐Lemaître‐Robertson‐Walker type. After a discussion of empty universes, the FLRW theory is extended with homogeneous scalar fields generically described by a σ‐model on some scalar manifold. An explicit gauge‐invariant solution is constructed for the non‐linear O(N)‐models.     

原子核天体物理简介*

文章对原子核天体物理这一门重要交叉学科作了简单的介绍,并以一批获得诺贝尔物理奖的成果为线索,重点描述了大爆炸宇宙学、太阳中微子、恒星演化及其终点以及原子核物理与元素的起源等方面的进展与挑战。     

The linearization method and new classes of exact solutions in cosmology

We develop a method for constructing exact cosmological solutions of the Einstein equations based on representing them as a second-order linear differential equation. In particular, the method allows using an arbitrary known solution to construct a more general solution parameterized by a set of 3N constants, where N is an arbitrary natural number. The large number of free parameters may prove useful for constructing a theoretical model that agrees satisfactorily with the results of astronomical observations. Cosmological solutions on the Randall-Sundrum brane have similar properties. We show that three-parameter solutions in the general case already exhibit inflationary regimes. In contrast to previously studied two-parameter solutions, these three-parameter solutions can describe an exit from inflation without a fine tuning of the parameters and also several consecutive inflationary regimes. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 2, pp. 312–320, February, 2009.     

General Properties of Cosmological Models with an Isotropic Singularity

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a -law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show that the Isotropic Singularity is a point-like singularity and that vacuum space-times cannot admit an Isotropic Singularity. The relationships between the Isotropic Singularity, and the energy conditions, and the Hubble parameter is explored. A review of work by the authors, regarding the Isotropic Singularity, is presented.     

Causality in Inflationary Universes with Positive Spatial Curvature

We show that in the case of positively-curved Friedmann-Lemaître universes (k = +1), an inflationary period in the early universe will for most initial conditions not solve the horizon problem, no matter how long inflation lasts. It will only do so for cases where inflation starts in an almost static state, corresponding to an extremely high value of , 1, at the beginning of inflation. For smaller values, it is not possible to solve the horizon problem because the relevant integral asymptotes to a finite value (as happens also in the de Sitter universe in a k = +1 frame). Thus, for these cases, the causal problems associated with the near-isotropy of the Cosmic Background Radiation have to be solved already in the Planck era. Furthermore both compact space sections and event horizons will exist in these universes even if the present cosmological constant dies away in the far future, raising potential problems for M-theory as a theory of gravity.     

Kinematics of a Spacetime with an Infinite Cosmological Constant

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant is discussed by using Inönü–Wigner contractions of the de Sitter groups and spaces. When , spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c is further considered, the kinematical group in this case being a modified Galilei group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology.