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Astron. Astrophys. 344, 735-743 (1999)

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Topological lens effects in universes with non-euclidean compact spatial sections

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

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

Received 17 November 1998 / Accepted 8 January 1999

Abstract

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 spaces, as a function of the cosmological parameters, of the volume of the spatial sections and of the catalog depth. Next we apply the crystallographic method, aimed to detect a topological signal in the 3D distance histogram between images, to compact hyperbolic models. Numerical calculations in the Weeks manifold allow us to check the absence of crystallographic signature of topology, due to the fact that the number of copies of the fundamental domain in the observable covering space is low and that the points are not moved the same distance by the holonomies of space.

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

Send offprint requests to: R. Lehoucq

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© European Southern Observatory (ESO) 1999

Online publication: March 29, 1999
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