Related papers: General Topology of the Universe
Questions such as whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental open problems that high precision modern cosmology needs to resolve. These questions go beyond the scope of…
General relativity is unable to determine the topology of the Universe. We propose to apply quantum approach. Quantization of dynamics of a test particle is sensitive to the spacetime topology. Presented results for a particle in de Sitter…
If the topology of the universe is compact we show how it significantly changes our assessment of the naturalness of the observed structure of the universe and the likelihood of its present state of high isotropy and near flatness arising…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
Quel est, ou pourrait \^etre, la topologie globale de la partie spatiale de l'Univers ? L'Univers entier (pr\'ecis\'ement, l'hypersurface spatiale de celui-ci) est-il observable ? Les math\'ematiciens, les physiciens et les cosmologistes…
Current evidence suggests that the cosmological constant is not zero, or that we live in an open universe. We examine the implications for the future under these assumptions, and find that they are striking. If the Universe is cosmological…
Clues as to the geometry of the universe are encoded in the cosmic background radiation. Hot and cold spots in the primordial radiation may be randomly distributed in an infinite universe while in a universe with compact topology…
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand…
``One could imagine that as a result of enormously extended astronomical experience, the entire universe consists of countless identical copies of our Milky Way, that the infinite space can be partitioned into cubes each containing an…
All inhabitants of this universe, from galaxies to people, are finite. Yet the universe itself is often assumed to be infinite. If instead the universe is topologically finite, then light and matter can take chaotic paths around the compact…
The space-like hypersurface of the Universe at the present cosmological time is a three-dimensional manifold. A non-trivial global topology of this space-like hypersurface would imply that the apparently observable universe (the sphere of…
Is the Universe (a spatial section thereof) finite or infinite? Knowing the global geometry of a Friedmann-Lema\^{\i}tre (FL) universe requires knowing both its curvature and its topology. A flat or hyperbolic (``open'') FL universe is {\em…
Conventional thinking says the universe is infinite. But it could be finite and relatively small, merely giving the illusion of a greater one, like a hall of mirrors. Recent astronomical measurements add support to a finite space with a…
The spacetime structure of the spatially uniformly expanding universe is described in terms of a kind of global space and global time instead of the space and time we usually recognize. The global space at some instant is a space in which…
What is the shape of the Universe? Is it finite or infinite ? Is space multi-connected to create ghost images of faraway cosmic sources? After a "dark age" period, the field of cosmic topology has now become one of the major concerns in…
The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…
Based on the conjecture that rather than the second law of thermodynamics inevitably be breached as matter approaches a big crunch or a black hole singularity, the order of events should reverse, a model of the universe that resolves a…
The Hilbert-Einstein equations are insufficient to describe the geometry of the Universe, as they only constrain a local geometrical property: curvature. A global knowledge of the geometry of space, if possible, would require measurement of…
We clarify the confusion, misunderstanding and misconception that the physical finiteness of the universe, if the universe is indeed finite, would rule out all hypercomputation, the kind of computation that exceeds the Turing computability,…
It is proposed that the physical universe is an instance of a mathematical structure which possesses a dual structure, and that this dual structure is the collection of all possible knowledge of the physical universe. In turn, the physical…