Cosmic crystallography.
Abstract
We assume that the Universe has a non trivial topology whose compact spatial sections have a volume significantly smaller than the horizon volume. By a topological lens effect, such a "folded" space configuration generates multiple images of cosmic sources, e.g. clusters of galaxies. We present a simple and powerful method to unveil non ambiguous observational effects, independently of the sign of the curvature and of the topological type. By analogy with techniques used in crystallography, we look for spikes in the pair separation histogram between cosmic objects in 3D space. The spikes due to multiconnectedness should stand out dramatically. Moreover, their positions and their relative amplitudes would be definite signatures of the topological type and of the underlying geometry. Such a statistical method would thus reveal the shape of space. As illustrative examples, we perform numerical simulations in {OMEGA}=1 Friedmann universes with the six possible closed orientable topologies, which prove the efficiency of our method. Presently available 3D catalogs of galaxy clusters are not deep enough to test our method at sizes greater than lower limits =~600h^1^Mpc previously obtained by other methods. With extensive redshift surveys currently in progress the situation may change in the next decade.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 September 1996
 DOI:
 10.48550/arXiv.grqc/9604050
 arXiv:
 arXiv:grqc/9604050
 Bibcode:
 1996A&A...313..339L
 Keywords:

 COSMOLOGY: LARGE SCALE STRUCTURE OF UNIVERSE;
 MISCELLANEOUS;
 METHODS: MISCELLANEOUS;
 General Relativity and Quantum Cosmology;
 Astrophysics
 EPrint:
 to appear in Astronomy and Astrophysics. Contains 11 pages, 14 Postscript figures, use A&