If you try to examine the long line by selecting a piece of it, say a,b, then this piece looks like an ordinary interval but almost all of the line is outside this piece. U nofthem, the cartesian product of u with itself n times. To be fully rigorous we should point out that even though the individual dot products di follow the same. Metricandtopologicalspaces university of cambridge. The curvature of any locally isotropic space and hence of a locally isotropic universe falls into one of the three following cases. Dodecahedral space topology as an explanation for weak wideangle temperature correlations in the cosmic microwave background by jean pierre luminet, j weeks, a riazuelo, r lehoucq and j p uzan abstract. We also have the following simple lemma lemma 3 a subset u of a metric space is open if and only if it is a neighbor hood of each of its points. The poincare dodecahedral space model gains support to.
In this paper we settle thurstons old question of whether the weberseifert dodecahedral space is nonhaken, a problem that has been a benchmark for progress in computational 3manifold topology over recent decades. The dodecahedral space is a manifold of genus 2 with a seifert fibration and is the only known poincare space with finite fundamental group. Luminet jp1, weeks jr, riazuelo a, lehoucq r, uzan jp. A test of the poincare dodecahedral space topology. The poincare dodecahedral space model gains support to explain the shape of space an international team of cosmologists, led by a researcher from paris observatory, has improved the theoretical pertinence of the poincare dodecahedral space pds topology to explain some observations of the cosmic microwave background cmb. Dodecahedral space topology as an explanation for weak wideangle temperature correlations in the cosmic microwave background jeanpierre luminet 1 jeffrey r. The spectral action functional, considered as a model of. Dodecahedral space topology as an explanation for weak wideangle temperature correlations in the cosmic microwave background jeanpierre luminet1, jeffrey r. Jeff weeks has posted a flight simulator allowing one to navigate around the manifold, and moreover has explained in the notices how it may be linked. Pdf monopole floer homology, eigenform multiplicities. Pdf the status of cosmic topology after planck data. I just checked using snappea that there is a cover of the seifertweber dodecahedral space of index 25 a 5fold cyclic cover of a 5fold cyclic cover which has positive first betti number hence is haken. Consider the intersection eof all open and closed subsets of x containing x. Pdf the shape and topology of the universe researchgate.
Cosmologys standard model posits an infinite flat universe forever expanding under the pressure of dark energy. Orbifold construction of the modes of the poincare. We show that the seifertweber dodecahedral space sw is an l space. Oct 09, 2003 cosmologys standard model posits an infinite flat universe forever expanding under the pressure of dark energy. If you have a pair of redblue glasses, turn off fog, turn on stereo, and start flying around. Aurich et al have recently posted a more comprehensive paper, based on more detailed simulations, that confirms these results for the dodecahedral space while finding analogousbut slightly differentresults for a variety of other topologies. We show that the seifertweber dodecahedral space sw is an lspace. Spherical dodecahedral space as constructed here inherits a geometry from the dodecahedron. If one remains inside what was the 3dimensional interior of the dodecahedron, geometrical calculations go exactly as they do in 3dimensional euclidean space. Extrinsic topology is concerned with properties of a surface or manifold seen from an external viewpoint. The curvature is a quantity describing how the geometry of a space differs locally from the one of the flat space. Dodecahedral space topology as an explanation for weak. Download the curved spaces software and open the sample file hyperbolicsmall. Shape of the universe from the status of cosmic topology after planck data 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 planck telescopes.
Notes on metric spaces these notes are an alternative to the textbook, from and including closed sets and open sets page 58 to and excluding cantor sets page 95 1 the topology of metric spaces assume m is a metric space with distance function d. Here we present a simple geometrical model of a finite, positively curved space the poincar\e dodecahedral space which accounts for wmaps observations with no finetuning required. We discuss more particularly the proposal of a finite, positively curved, dodecahedral space for explaining some puzzling features of the cosmic microwave. Pdf dodecahedral space toplogy as an explanation for. The local features of the geometry of the universe are primarily described by its curvature, whereas the topology of the universe describes general global properties of its shape as of a continuous object. Youll see a tiling of the hyperbolic space by infinitely many copies of a small polyhedron. We study observational constraints on models that account for the accelerated expansion of the universe via infrared modifications to general relativity, namely the dvaligabadadzeporrati braneworld model as well as the dvaliturner and cardassian models. Section 3 is dedicated to proving that the poincare dodecahedral space does in fact result from identifying faces of a dodecahedron in a certain way. We then looked at some of the most basic definitions and properties of pseudometric spaces. Temperature correlations across the microwave sky match expectations on scales. Physicsworld references dodecahedral space topology as an explanation for weak wideangle temperature correlations in the cosmic microwave background by j.
Observational constraints on modified gravity models and. 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 planck telescopes. Its fundamental group is known as the binary icosahedral group and has order 120. The ordinary line r is homeomorphic to an open interval. Cosmic topology involves both global topological features and more local geometrical properties such as curvature. Poincare dodecahedral space and the qi men dun jia model. Its connected components are singletons,whicharenotopen. A dodecahedral space is the orbit space of the free action of a binary icosahedron group on the threedimensional sphere. Introduction in chapter i we looked at properties of sets, and in chapter ii we added some additional structure to a set a distance function to create a pseudomet. The spectral action and cosmic topology matilde marcolli, elena pierpaoli, and kevin teh in memory of andrew lange abstract.
Even though hyperbolic space is much roomier than flat space, your stereoscopic vision. Their paper is titled dodecahedral space topology as an explanation for weak wideangle temperature correlations in the cosmic microwave background. A test of the poincare dodecahedral space topology hypothesis. Pdf dodecahedral space toplogy as an explanation for weak. Cmb data suggest spherical space with dodecahedral topology.
The seifertweber space is a 5fold cyclic branched cover over the whitehead link complement. Jp luminet, jr weeks, a riazuelo, r lehoucq, jp uzan, dodecahedral space topology as an explanation for weak wideangle temperature correlations in the cosmic microwave background, nature 425 2003 593595 nicholas jackson poincar e dodecahedral space. If v,k k is a normed vector space, then the condition du,v ku. In vedic nuclear physics, the number 28 plays a key role, and this will be discussed in a future paper. The 28 aspects must be extruded or dispersed along structures which contain factors of. Spherical dodecahedral space is one of my favorite 3dimensional manifolds. We overcome this by exploiting the large symmetry group and the arithmetic and tetrahedral. Just choose klein bottle from the games topology menu.
The spectral action functional, considered as a model of gravity coupled to matter, provides, in its nonperturbative form, a slowroll potential for infla we explicitly compute the nonperturbative spectral action for some of the main candidates for cosmic topologies, namely the quaternionic space, the poincare dodecahedral space, and the. The universe as a phibased dodecahedron the golden. Dodecahedral space toplogy as an explanation for weak wideangle temperature correlations in the cosmic microwave background article pdf available in nature 4256958. New findings in 2003 reveal that the shape of the universe is a dodecahedron based on phi. The epitahedron, a newly discovered heptahedron, is assigned as the 3dimensional representation of the penrose kites and darts. When 3d torus games become available, therell be an option for nonorientable spaces as well. Dodecahedral space topology as an explanation for weak wideangle temperature correlations in the cosmic microwave background. Lost in space a multiconnected dodecahedral universe gives the. The poincare dodecahedral space and the mystery of the. The 28 aspects must be extruded or dispersed along structures which contain factors of 12 or 6. Firstyear data from the wilkinson microwave anisotropy probe wmap confirm this model to spectacular precision on all but the largest scales bennett \\it et al.
The concept of an inner product occurs both in algebra and in many physics courses. The spectral action and cosmic topology springerlink. Thus epitahedra are tiling the space in the golden ratio analogous to the. The spectral action functional, considered as a model of gravity coupled to matter, provides, in its nonperturbative form, a slowroll potential for inflation, whose form and corresponding slowroll parameters can be sensitive to the underlying cosmic topology. Pdf a test of the poincare dodecahedral space topology. Lehoucq, dodecahedral space topology as an explanation for weak wideangle temperature correlations in the cosmic microwave background, nature 425 2003 593595. But the long line is not homeomorphic to any subset of rn because it is not second countable. We explicitly compute the nonperturbative spectral action for some of the main candidates for cosmic topologies, namely the. An excess in the correlation of the identified circles was reported by r04, for circles of angular radius of 11 for a relative. A configuration space is a topological object that can be used to study the allowable states of a given system. Being a spherical 3manifold, it is the only homology 3sphere besides the 3sphere itself with a finite fundamental group. The shape of the universe, in physical cosmology, is the local and global geometry of the universe.
A test of the poincare dodecahedral space topology hypothesis with the wmap cmb data article pdf available in astronomy and astrophysics 4823 february 2008 with 36 reads how we measure reads. It has been suggested by roukema and coworkers hereafter r04 that the topology of the universe as probed by the matched circles method using the first year release of the wmap cmb data, might be that of the poincare dodecahedral space pds model. The long line richard koch november 24, 2005 1 introduction. Matilde marcolli the spectral action and cosmic topology. Dodecahedral topology fails to explain quadrupoleoctupole. The poincare homology sphere also known as poincare dodecahedral space is a particular example of a homology sphere, first constructed by henri poincare. Our universe might be a poincar e dodecahedral space.
Dodecahedral space topology as an explanation for weak wide. Circle searching cornish, spergel and starkman, 1998 may confirm the models topological predictions, while upcoming planck surveyor data may confirm its. Its big brother, hyperbolic dodecahedral space, had a starring role in the geometry center movie not knot, but spherical has had some publicity of its own. Introduction cosmic topology 4 considers big bang models where space is multiconnected, rather than.
In this description, hyperbolic space does not seem to have any preferred origin, but appears to have a preferred direction. The euler characteristic is a topological invariant. The video the shape of space constructs the klein space and takes you on a computeranimated flight. We find that significant constraints can be placed on the parameters of each model using type ia supernovae data together with the baryon. Pdf monopole floer homology, eigenform multiplicities and. A direct application of our previous techniques runs into difficulties arising from the computational complexity of the problem. Oct 09, 2003 dodecahedral space topology as an explanation for weak wideangle temperature correlations in the cosmic microwave background. Like visible light from distant stars and galaxies, cosmic background radiation allows scientists to peer into the past to the time when the universe was.
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