相关论文: Three-dimensional Topology-Independent Methods 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…
The Universe is a physical object. Physical objects have shapes and sizes. General relativity is insufficient to describe the global shape and size of the Universe: the Hilbert-Einstein equations only treat limiting quantities towards an…
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…
Suppose we have identified three clusters of galaxies as being topological copies of the same object. How does this information constrain the possible models for the shape of our Universe? It is shown here that, if the Universe has flat…
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…
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…
We assume that the Universe has a non trivial topology whose compact spatial sections have a volume significantly smaller than the horizon volume. By a topological lens effect, such a "folded" space configuration generates multiple images…
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…
If the universe has a nontrivial shape (topology) the sky may show multiple correlated images of cosmic objects. These correlations can be couched in terms of distance correlations. We propose a statistical quantity which can be used to…
A nontrivial topology of the spatial section of the universe is an observable, which can be probed for all locally homogeneous and isotropic universes, without any assumption on the cosmological density parameters. We discuss how one can…
This review aims to cover the central aspects of current research in cosmic topology from a topological and observational perspective. Beginning with an overview of the basic concepts of cosmology, it is observed that though a determinant…
``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…
This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…
The large scale geometry of the late Universe can be decomposed as R$\times {\Sigma}_3$, where R stands for cosmic time and ${\Sigma}_3$ is the three dimensional spatial manifold. We conjecture that the spatial geometry of the Universe's…
When the density parameter is close to unity, the universe has a large curvature radius independently of its being hyperbolic, flat, or spherical. Whatever the curvature, the universe may have either a simply connected or a multiply…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
A flat Universe model supported by recent observations has 18 possible choices for its overall topology. To detect or exclude these possibilities is one of the most important tasks in modern cosmology, but it has been very difficult for…
It seems to be a common belief that the space in which we live is a space-time manifold of dimension at least four. In the present article we wish to draw attention to a slightly different possibility - a space-time pseudomanifold (or even…
Recent studies of the detectability of cosmic topology of nearly flat universes have often concentrated on the range of values of $\Omega_{0}$ given by current observations. Here we study the consequences of taking the bounds on…