Related papers: Signature for the Shape of the Universe
Two procedures for obtaining (extracting and constructing) the topological signature of any multiply connected Robertson-Walker (RW) universe are presented. It is shown through computer-aided simulations that both approaches give rise to…
A statistical quantity suitable for distinguishing simply-connected Robertson-Walker (RW) universes is introduced, and its explicit expressions for the three possible classes of simply-connected RW universes with an uniform distribution of…
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…
Observations of microwave background fluctuations can yield information not only about the geometry of the universe, but potentially about the topology of the universe. If the universe is negatively curved, then the characteristic scale for…
Given the wealth of increasingly accurate cosmological observations, especially the recent results from the WMAP, and the development of methods and strategies in the search for cosmic topology, it is reasonable to expect that we should be…
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…
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…
A non-trivial spatial topology of the Universe is a potentially observable attribute, which can be probed through the circles-in-the-sky for all locally homogeneous and isotropic universes with no assumptions on the cosmological parameters.…
Multi-connected universe models with space identification scales smaller than the size of the observable universe produce topological images of cosmic sources. We generalise to locally hyperbolic spaces the crystallographic method, aimed 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…
We reexamine the possibility of the detection of the cosmic topology in nearly flat hyperbolic Friedmann-Lemaitre-Robertson-Walker (FLRW) universes by using patterns repetition. We update and extend our recent results in two important ways:…
In order to include nontrivial spatial topologies in the problem of quantum creation of a universe, it seems to be necessary to generalize the sum over compact, smooth 4-manifolds to a sum over finite-volume, compact 4-orbifolds. We…
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…
We present a method to search for large angular-scale correlations, termed topological signatures, in the angular distribution of cosmic objects, which does not depend on cosmological models or parameters and is based only on the angular…
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…
If the universe is finite and smaller than the distance to the surface of last scatter, then the signature of the topology of the universe is writ large on the microwave background sky. We show that the microwave background will be…
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…
Universe models with compact spatial sections smaller than the observable universe produce a topological lens effect. Given a catalog of cosmic sources, we estimate the number of topological images in locally hyperbolic and locally elliptic…
[Abridged] An observable signature of a detectable nontrivial spatial topology of the Universe is the circles-in-the-sky in the CMB sky. In the most general search, pairs of circles with deviation from antipodality $0^\circ \leq \theta \leq…
If the universe is finite and smaller than the distance to the surface of last scatter, then the signature of the topology of the universe is writ on the microwave background sky. Previous efforts to search for this topology have focused on…