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Astron. Astrophys. 351, 766-774 (1999)

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A new crystallographic method for detecting space topology

J.-Ph. Uzan 1,2, R. Lehoucq 3 and J.-P. Luminet 2

1 Département de Physique Théorique, Université de Genève, 24 quai E. Ansermet, 1211 Geneva, Switzerland (uzan@amorgos.unige.ch)
2 Département d'Astrophysique Relativiste et de Cosmologie, Observatoire de Paris, CNRS-UPR 176, 92195 Meudon, France (Jean-Pierre.Luminet@obspm.fr)
3 CE-Saclay, DSM/DAPNIA/Service d'Astrophysique, 91191 Gif sur Yvette cedex, France (roller@discovery.saclay.cea.fr)

Received 15 March 1999 / Accepted 19 July 1999

Abstract

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 detect the topology from three-dimensional catalogs of cosmological objects. Our new method is based on the construction of a collecting-correlated-pair technique which enhances the topological signature and can make it detectable. The main idea is that in multi-connected universes, equal distances occur more often than by chance. We present an idealised version of this method as well as numerical simulations, we discuss the statistical relevance of the expected signature and we show how the extraction of a topological signal may also lead to a precise determination of the cosmological parameters. A more realistic version of the method which takes account of uncertainties in the position and velocity data is then discussed. We apply our technique to presently available data, namely a quasar catalog, and discuss the significance of the result. We show how the improved crystallographic method both competes with the two-dimensional methods based on cosmic microwave background analyses, and suffers from the same drawback: the shortage of present observational data.

Key words: cosmology: theory – cosmology: large-scale structure of Universe

Send offprint requests to: J.-Ph. Uzan

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© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999
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