On topological aspects of the birth of the universe

The topological requirements are considered of extending matter fields in a three-dimensional universe to the whole compact four-manifold in quantum cosmology. In some cases, especially in the Skyrme model, the winding number of matter fields φ must be zero for a large class of manifolds.     

Bubble dynamics in the expanding universe

Using the Gauss-Codazzi equations, the behavior of a singular hypersurface, which divides the universe into two Friedmann-Robertson-Walker space-time regionsV ⁺ andV ^–, is investigated. The equation of motion for a spherical bubble in the expanding universe is presented and the physical meaning of the equation is clarified. The equations of state for fluids inV ^± and on the boundary shell, which should be determined by microscopic physics, are arbitrary in the present geometrical approach. The derived equations are quite similar to those for a shell in a vacuum and can be applied to the case that one ofV ^± or both are Schwarzschild-de Sitter space-time too.     

VI. Dynamical and topological considerations of quark confinement

Non-Abelian magnetic superconductivity provides a realisation of the topological algebra of 't Hooft which does confine quarks. Its dynamical and topological aspects are discussed and the related phenomenological theory of quark confinement is sketched.     

The tilted universe

The simplest interpretation of the CMBR dipole anisotropy is that it arises due to our motion with respect to the cosmic rest frame. However, the existence of a superhorizon-sized isocurvature perturbation can give rise to a dipole anisotropy intrinsic to the CMBR. In this case the cosmic rest frame and the CMBR rest framedo not coincide, and when viewed from the CMBR rest frame the universe appears tilted: matter streams uniformly from one side of the universe to the other. The intrinsic dipole model provides an explanation for the puzzling observation that most of the matter within a l00^–1 Mpc cube centered on our galaxy has a large velocity (of order 600 km s^–1) with respect to the CMBR rest frame.This essay received the first award from the Gravity Research Foundation, 1991—Ed.     

The causal universe

Creation of matter is possible in the cosmological context, without cost of energy. This creation is regulated by the laws of quantum mechanics and general relativity. These elements are used to conceive a singularity-free causal open homogeneous isotropic cosmology. The history of the universe unfolds in two stages: the fireball production stage, which occurs as the response to a spontaneous local disturbance, is followed by free expansion. The latter extrapolates back to the former to avoid the initial big-bang singularity.This essay was awarded the first prize for 1978 by the Gravity Research Foundation. (Ed.)     

The deformable universe

The concept of smooth deformations of Riemannian manifolds, recently evidenced by the solution of the Poincaré conjecture, is applied to Einstein’s gravitational theory and in particular to the standard FLRW cosmology. We present a brief review of the deformation of Riemannian geometry, showing how such deformations can be derived from the Einstein-Hilbert dynamical principle. We show that such deformations of space-times of general relativity produce observable effects that can be measured by four-dimensional observers. In the case of the FLRW cosmology, one such observable effect is shown to be consistent with the accelerated expansion of the universe.     

The computing universe

In theoretical physics the concept of “field” is often applied to various phenomena in the space, normally represented by differential equations. In contrast to that, the theory of automata operates with discrete states. In this, the digitalization of procedures is an important aspect. Cellular automata allow the construction of “moving state structures” representing digital particles, which may be compared with the behavior of physical particles. The theory of automata further presupposes certain attitudes towards determination and causality. In close connection is the problem of the reversibility of time direction.     

第四讲暴涨宇宙学的研究与进展

文章简单介绍了标准(大爆炸)宇宙模型的成功和困难，着重介绍了暴涨宇宙学的研究历史和最近的进展，并展望了今后人们可能的关注方向     

Network ecology: topological constraints on ecosystem dynamics

Ecological systems are complex assemblages of various species with interactions between them. The interactions can be even more important than the species themselves for understanding how the whole system is functioning and organized. For the representation of the topological space of interspecific relationships, graph theory is a suitable mathematical tool: the network perspective and the various techniques of network analysis are more and more elaborated and invading ecology. Beyond a static view on networks, fundamental questions can only be answered if dynamical analyses are also made, and now it is clear that structural and dynamical studies must not “compete” but strongly complement each other. Our aim is to give a menu of classical and more recently suggested network indices and to discuss what do we know about their relations to ecosystem dynamics. Since ecologists have very diverse problems, they need diverse techniques and a good insight in matching the adequate method to a particular problem. The main question is how to link certain graph properties to understanding and predicting the behaviour of an ecosystem. We wish to contribute to bridging the gap between extreme structural and extreme dynamical views.     

The evolution of the universe from non-compact Kaluza-Klein theory

We develop a 5D mechanism, inspired by Campbells theorem, to explain the (neutral scalar field governed) evolution of the universe from an initially inflationary expansion that has a change of phase towards a decelerated expansion and thereafter evolves towards the present day observed accelerated (quintessential) expansion.Received: 4 October 2004, Published online: 23 November 2004PACS: 04.20.Jb, 11.10.Kk, 98.80.Cq     

The universe: A birth far from equilibrium?

The scientific world is, as I have often repeated, a shadow world, shadowing a world familiar to our consciousness. Just how much do we expect it to shadow? We do not expect it to shadow all that is in our mind, emotions, memory, etc. In the main we expect it to shadow impressions which can be traced to external sense organs. But time makes a dual entry and thus forms an intermediate link between the internal and the external. This is shadowed partially by the scientific world of primary physics (which excludes time's arrow), but fully when we enlarge the scheme to include entropy. Therefore by the momentous departure in the nineteenth century the scientific world is not confined to a static extension around which the mind may spin a romance of activity and evolution; it shadows that dynamic quality of the familiar world which cannot be parted from it without disaster to its significance.—Arthur Eddington,The Nature of the Physical World.     

The early Weyl universe

The consequences of a period of Weyl invariance in the early universe are investigated. It is argued that the natural outcome of such a period is a Kaluza-Klein style compactification of an internal space in which any time variation of the scale factor of this space is absorbed (via a Weyl transformation) into the gravitational coupling. A five-dimensional test model is shown to undergo exponential inflation of the space-time sector due to a false vacuum state of the non-metric part of the connection.     

The warm inflationary universe

In the past decade, the importance of dissipation and fluctuation to inflationary dynamics has been realized and has led to a new picture of inflation called warm inflation. Although these phenomena are common to condensed matter systems, for inflation models their importance has only recently started to be appreciated. The article describes the motivation for these phenomena during inflation and then examines their origins from first principles quantum field theory treatments of inflation models. Cosmology today is a data intensive field and this is driving theory to greater precision and predictability. This opens the possibility to consider tests for detecting observational signatures of dissipative processes, which will be discussed. In addition, it will be discussed how particle physics and cosmology are now working in tandem to push the boundaries of our knowledge about fundamental physics.     

The entangled accelerating universe

Using the known result that the nucleation of baby universes in correlated pairs is equivalent to spacetime squeezing, we show in this Letter that there exists a T-duality symmetry between two-dimensional warp drives, which are physically expressible as localized de Sitter little universes, and two-dimensional Tolman–Hawking and Gidding–Strominger baby universes respectively correlated in pairs, so that the creation of warp drives is also equivalent to spacetime squeezing. Perhaps more importantly, it has been also seen that the nucleation of warp drives entails a violation of the Bell's inequalities, and hence the phenomena of quantum entanglement, complementarity and wave function collapse. These results are generalized to the case of any dynamically accelerating universe filled with dark or phantom energy whose creation is also physically equivalent to spacetime squeezing and to the violation of the Bell's inequalities, so that the universe we are living in should be governed by essential sharp quantum theory laws and must be a quantum entangled system.