Bianchi Type I Universe Models with Irreversible Matter Creation

The effects of matter creation on the evolution and dynamics of an anisotropic Bianchi type I space–time is investigated in the framework of open thermodynamic systems theory. For a cosmological fluid obeying a Zel'dovich type equation of state =p and with particle creation rate proportional to the square of the mean Hubble function and to the energy density of matter, respectively, the general solution of the gravitational field equations can be expressed in an exact parametric form. Generically all models start from a non-singular state. In the large time limit anisotropic cosmological models with particle creation rate proportional to the square of the Hubble function end in an isotropic flat (inflationary or non–inflationary) phase while models with particle source function proportional to the energy density of matter do not isotropize, ending in a Kasner–type geometry.     

Conformal Invariance, Accelerating Universe and the Cosmological Constant Problem

We investigate a conformal invariant gravitational model which is taken to hold at early universe. The conformal invariance allows us to make a dynamical distinction between the two unit systems (or conformal frames) usually used in cosmology and elementary particle physics. In this model we argue that when the universe suffers phase transition, the resulting mass scale introduced by particle physics should have a variable contribution to vacuum energy density. This variation is controlled by the conformal factor which is taken as a dynamical field. We then deal with the cosmological consequences of this model. In particular, we shall show that there is an inationary phase at early times. At late times, on the other hand, it provides a mechanism which makes a large effective cosmological constant relax to a sufficiently small value. Moreover, we shall show that the conformal factor acts as a quintessence field that leads the universe to accelerate at late times.     

Vacuum Energy and the Economical Universe

We revisit a suggestion, first made by Haas and Jordan but often attributed to Tryon and others, that the universe could have zero net energy since a test body's positive rest energy is approximately cancelled out by its negative gravitational binding energy with respect to the rest of the matter in the universe. If the universe is not matter- but vacuum-dominated, as observations now indicate, then the balance between rest and binding energies is substantially altered. We consider whether this may make the Newtonian case for a universe from nothing more plausible than before.     

一类无奇点宇宙模型

按照Penrose-Hawking的奇点定理,在场源物质无旋、无加速且能量密度满足条件ρ+3p≥0的宇宙模型中一定存在奇点.本文研究了场源物质有旋时的无奇点宇宙模型,获得了几种无奇点的宇宙解.     

Geometric derivation of nonlinear sigma model for the 1D antiferromagnet

It is argued that a purely geometric derivation of the long-range action for the 1D antiferromagnet is available in terms of a Kähler potential. The derivation allows for a natural extension to the t-J model. In particular, it follows that a relevant long-wavelength action of the t-J model exhibits at least at the SUSY (J=2t) point the su(2∣1) invariance rather than the so(5) one.     

Bianchi Type-I Universe with wet dark fluid

The Bianchi Type-I Universe filled with dark energy from a wet dark fluid has been considered. A new equation of state for the dark energy component of the Universe has been used. It is modeled on the equation of state p = γ(ρ − ρ*) which can describe a liquid, for example water. The exact solutions to the corresponding field equations are obtained in quadrature form. The solution for constant deceleration parameter have been studied in detail for both power-law and exponential forms. The cases γ = 1 and γ = 0 have also been analysed.      

A Quantum Universe and the Solution to the Cosmological Problems

We have found that the hierarchial problems appearing in cosmology are a manifestation of the quantum nature of the universe. The universe is still described by the same formulae that once hold at Planck's time. The universe is found to be governed by the Machian equation, GM = Rc ², where M and R are mass and radius of the universe. A Planck's constant xsfor different cosmic scales is provided. The status of the universe at different stages is shown to be described in terms of the fundamental constants (c, , G, , H) only. The concept of maximal (minimal) acceleration, power, temperature, etc., is introduced and justified.     

Matching Spherical Dust Solutions to Construct Cosmological Models

Conditions for smooth cosmological models are set out and applied to inhomogeneous spherically symmetric models constructed by matching together different Lemaître–Tolman–Bondi solutions to the Einstein field equations. As an illustration the methods are applied to a collapsing dust sphere in a curved background. This describes a region which expands and then collapses to form a black hole in an Einstein de Sitter background. We show that in all such models if there is no vacuum region then the singularity must go on accreting matter for an infinite LTB time.     

Cosmological Relics of the High Energy Cold Dark Matter Particle in the Universe

We demonstrate that if the universe is dominated by the massive cold dark matter, then besides the generally believed thermal distribution of the dark matter relics, there may exist some very energetic nonthermal relics of the dark matter particles in the universe from some unknown sources, such as from decay of supermassive X particle released from topological defect collapse or annihilation. Very interesting, we point out that these high energy dark matter particles may be observable in the current and future cosmic ray experiments.     

On the stochasticity in relativistic cosmology

It was shown earlier by I. M. Lifshitz and two of us that the evolution of the relativistic cosmological models towards the singularity undergoes spontaneous stochastization.⁽¹⁾ In the present paper it is shown that the statistical parameters of this evolution can be calculated in an exact manner. From the point of view of the general ergodic theory we deal here with a specific mode of stochastization of a deterministic dynamical system with a five-dimensional phase space. The knowledge of the source of stochasticity makes it possible to develop a quantitative statistical theory with appreciable completeness.     

Pohlmeyer reduction of superstring sigma model

Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS₅×S⁵ superstring world-sheet theory in terms of physical degrees of freedom we construct the “Pohlmeyer-reduced” version of the corresponding sigma model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting equations can be obtained from a Lagrangian of a non-Abelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. A gauge-fixed form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. The small-fluctuation spectrum near the trivial vacuum contains 8 bosonic and 8 fermionic degrees of freedom with equal mass. We conjecture that the reduced model has world-sheet supersymmetry and is ultraviolet-finite. We show that in the special case of the AdS₂×S² superstring model the reduced theory is indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.     

No periodic orbits for the type A Bianchi's systems

It is known that the 6 models of Bianchi class A have no periodic solutions. In this article we provide a new, direct, unified and easier proof of this result.     

与额外维相关的膜宇宙模型

对引力场的能量\|动量和角动量守恒定律研究进展进行了总结。依此探讨了一般五维时空膜宇宙模型中的能量\|动量张量、 角动量张量以及它们的守恒定律。通过计算一个膜宇宙模型中的能动张量, 论证了该模型中“可见膜”上的引力非常弱, 这可认为是从引力的角度反映了规范层次问题。结果与一般的结论, 即引力系统总能量为零是一致的。同时, 分析了这个膜宇宙模型中的角动量张量, 计算了该模型中的总角动量, 讨论了暴涨Randall\|Sundren(RS)模型中的总角动量的一些性质。说明了在这类模型中总角动量的类空分量均为零, 这与普通RS模型是一样的。同时, 分析了RS模型中背景以及膜上的宇宙学常数, 发现在RS模型中五维背景宇宙学常数和两个膜上的真空能都能取它们的自然值。最后通过修改RS模型, 得到了一种可以产生很小的有效宇宙学常数的机制。We summarized both the general covariant energy\|momentum and angular momentum conservation law in the gravitational system and analyzed the general covariant energy\|momentum tensor of the gravitational system in general five\|dimensional cosmological in brane\|universe models. After calculating this energy\|momentum for the cosmological generalization of the Randall\|Sundrum(RS) model which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the “visible” brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy. We also discussed the properties of the general covariant angular momentum in five\|dimensional brane-universe model. With calculation of the total angular momentum of this model, we analyzed the properties of the total angular momentum in the inflationary RS model. We pointed that the space-like components of the total angular momentum are zero while the others are non-zero, which agrees with the results from ordinary RS model. We also investigated the bulk cosmological constant and brane vacuum energies in RS model. We show that the five\|dimensional bulk cosmological constant and the vacuum energies of the two branes could take their natural values. Finally we argued how we can generate a small four-dimensional effective cosmological constant on the branes by modifying the original RS model.     

Probing the anisotropic distribution of baryon matter in the Universe using fast radio bursts

We propose that fast radio bursts (FRBs) can be used as probes to constrain the possible anisotropic distribution of baryon matter in the Universe. Monte Carlo simulations show that 400 (800) FRBs are sufficient to detect the anisotropy at a 95% (99%) confidence level if the dipole amplitude has an order of magnitude of 0.01. However, more FRBs are required to tightly constrain the dipole direction. Even 1000 FRBs are insufficient to constrain the dipole direction within the angular uncertainty \begin{document}$\Delta\theta<40^{\circ}$\end{document} at a 95% confidence level. The uncertainty on the dispersion measure of a host galaxy does not significantly affect the results. However, if the dipole amplitude is in the region of 0.001, 1000 FRBs are not enough to correctly detect the anisotropic signal.     

Cosmological Constant and Stability of the Cosmological Models

The importance of cosmological constant for the cosmological models is given. The variations of the cosmological model for parameters λ and k were discussed respectively. Near λ = 0, the cosmological model is unstable with the change of λ, and near λ = β = 0, the cosmological model is unstable with the change of k. So when we consider the stable cosmological model, we must consider the nonzero cosmological constant.     

Local thermal equilibrium and ideal gas Stephani universes

The Stephani universes that can be interpreted as an ideal gas evolving in local thermal equilibrium are determined. Five classes of thermodynamic schemes are admissible, which give rise to five classes of regular models and three classes of singular models. No Stephani universes exist representing an exact solution to a classical ideal gas (one for which the internal energy is proportional to the temperature). But some Stephani universes may approximate a classical ideal gas at first order in the temperature: all of them are obtained. Finally, some features about the physical behavior of the models are pointed out.This revised version was published online in April 2005. The publishing date was inserted.     

Integrable multicomponent perfect fluid multidimensional cosmology. I

Multidimensional cosmological models with a space-time consisting ofn (n 2) Einstein spaces are investigated for a special class of multicomponent perfect fluid as a matter source. The dynamical behaviour of the universe is described. In the case of static internal spaces the external space evolves like a Friedmann universe with changing effective equation of state. Some of the models considered are integrable and classical as well as quantum solutions are found. Some of them represent wormholes. Quantum wormholes have a discrete spectrum.     

Study of Tachyon Warm Intermediate and Logamediate Inflationary Universe from Loop Quantum Cosmological Perspective

We have studied the tachyon intermediate and logamediate warm inflation in loop quantum cosmological background by taking the dissipative co-efficient Γ=Γ₀ (where Γ₀ is a constant) in “intermediate” inflation and Γ=V(φ), (where V(φ) is the potential of tachyonic field) in “logamediate” inflation. We have assumed slow-roll condition to construct scalar field φ, potential V, N-folds, etc. Various slow-roll parameters have also been obtained. We have analyzed the stability of this model through graphical representations.     

Letter: Self-Similar Bianchi Type VIII and IX Models

It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models the symmetry vector is not normal to the surfaces of spatial homogeneity. A direct consequence of this result is that there are no self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the most general Bianchi VIII and IX spacetime which admits a four dimensional group of homotheties is given.