Astron. Astrophys. 363, 1-8 (2000)

Limits of crystallographic methods for detecting space topology

R. Lehoucq ¹, J.-P. Uzan ^2,3 and J.-P. Luminet <sup>4

1</sup> CE-Saclay, DSM/DAPNIA/Service d'Astrophysique, 91191 Gif sur Yvette cedex, France (roller@discovery.saclay.cea.fr)
² Laboratoire de Physique Théorique, CNRS-UMR 8627, Bât. 210, Université Paris XI, 91405 Orsay cedex, France (uzan@th.u-psud.fr)
³ Département de Physique Théorique, Université de Genève, 24 quai E. Ansermet, 1211 Geneva, Switzerland
⁴ Département d'Astrophysique Relativiste et de Cosmologie, Observatoire de Paris, CNRS-UMR 8629, 92195 Meudon, France (Jean-Pierre.Luminet@obspm.fr)

Received 29 May 2000 / Accepted 4 July 2000

Abstract

We investigate to what extent the cosmic crystallographic methods aimed to detect the topology of the universe using catalogues of cosmic objects would be damaged by various observational uncertainties. We find that the topological signature is robust in the case of Euclidean spaces, but is very fragile in the case of compact hyperbolic spaces. Comparing our results to the presently accepted range of values for the curvature parameters, the best hopes for detecting space topology rest on elliptical space models.

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

Send offprint requests to: R. Lehoucq

This article contains no SIMBAD objects.

Contents

• 1. Introduction
  • 1.1. Notations and descriptions
• 2. Observational uncertainties
  • 2.1. Effects of peculiar velocities
  • 2.2. Effects of catalogue incompleteness
• 3. Numerical implementation
  • 3.1. Uncertainties on positions
  • 3.2. Catalogue incompleteness
• 4. General results
  • 4.1. Euclidean spaces
  • 4.2. Hyperbolic spaces
• 5. Conclusions and perspectives
• Acknowledgements
• References

© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000
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