Related papers: Detectability of Cosmic Topology in Flat Universes
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…
Recent observations suggest that the ratio of the total density to the critical density of the universe, $\Omega_0$, is likely to be very close to one, with a significant proportion of this energy being in the form of a dark component with…
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:…
Using recent observational constraints on cosmological density parameters, together with recent mathematical results concerning small volume hyperbolic manifolds, we argue that, by employing pattern repetitions, the topology of nearly flat…
[Abridged] In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations - the so-called circles-in-the-sky. Searches for…
The observed values of density parameters inevitably involve uncertainties. We study the conditions for detectability and undetectability of cosmic topology in presence of such uncertainties. We present closed analytical forms of…
An important, and potentially detectable, signature of a non-trivial topology for the universe is the presence of so called circles-in-the-sky in the cosmic microwave background (CMB). Recent searches, confined to antipodal and nearly…
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…
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…
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…
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…
[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…
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…
Whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental long-standing questions in cosmology. These questions of topological nature have become particularly topical, given the wealth of…
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 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…
In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations --- the so-called circles-in-the-sky. Searches undertaken for…
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…
Cosmic microwave background data shows the observable universe to be nearly flat, but leaves open the question of whether it is simply or multiply connected. Several authors have investigated whether the topology of a multiply connect…
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…