Related papers: Topological Pattern Formation
The universe displays a three-dimensional pattern of hot and cold spots in the radiation remnant from the big bang. The global geometry of the universe can be revealed in the spatial distribution of these spots. In a topologically compact…
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…
If the universe is multiply-connected and sufficiently small, then the last scattering surface wraps around the universe and intersects itself. Each circle of intersection appears as two distinct circles on the microwave sky. The present…
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…
We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product…
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…
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…
We study the effect of a finite topology on the temperature correlations of the cosmic microwave background in a flat universe. Analytic expressions for the angular power spectrum are given for all possible finite flat models. We examine…
The standard method for observationally confirming the existence of a predicted finite topology of the universe involves searching for the repetition of the same finite or extended source in different directions. However, serious problems…
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…
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…
What is the shape of space is a long-standing question in cosmology. In this talk I review recent advances in cosmic topology since it has entered a new era of experimental tests. High redshift surveys of astronomical sources and accurate…
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…
Topological defects are ubiquitous in condensed-matter physics but only hypothetical in the early universe. In spite of this, even an indirect evidence for one of these cosmic objects would revolutionize our vision of the cosmos. We give…
An introduction to modern theories for the origin of structure in the Universe is given. After a brief review of the growth of cosmological perturbations in an expanding Universe and a summary of some important observational results, the…
We study the effect of global topology of the spatial geometry on the cosmic microwave background (CMB) for closed flat and closed hyperbolic models in which the spatial hypersurface is multiply connected. If the CMB temperature…
In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB) obtained by WMAP and…
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…
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…
We investigate the behaviour of light rays in an open universe with a partly periodic horn topology. The geodesics can be solved exactly and the periodic topology creates characteristic new effects in temperature maps of the microwave…