Volume 529, May 2011
|Number of page(s)||12|
|Section||Cosmology (including clusters of galaxies)|
|Published online||15 April 2011|
An improved cosmic crystallography method to detect holonomies in flat spaces
Institute of Astronomy, School of Science, University of Tokyo, 2-21-1, Osawa, Mitaka, 181-0015 Tokyo, Japan
Received: 14 January 2011
Accepted: 2 March 2011
A new, improved version of a cosmic crystallography method for constraining cosmic topology is introduced. Like the circles-in-the-sky method using CMB data, we work in a thin, shell-like region containing plenty of objects. Two pairs of objects (quadruplet) linked by a holonomy show a specific distribution pattern, and three filters of separation, vectorial condition, and lifetime of objects extract these quadruplets. Each object Pi is assigned an integer si, which is the number of candidate quadruplets including Pi as their members. Then an additional device of si-histogram is used to extract topological ghosts, which tend to have high values of si. In this paper we consider flat spaces with Euclidean geometry, and the filters are designed to constrain their holonomies. As the second filter, we prepared five types that are specialized for constraining specific holonomies: one for translation, one for half-turn corkscrew motion and glide reflection, and three for nth turn corkscrew motion for n = 4,3, and 6. Every multiconnected space has holonomies that are detected by at least one of these five filters.Our method is applied to the catalogs of toy quasars in flat Λ-CDM universes whose typical sizes correspond to z ~ 5. With these simulations our method is found to work quite well. These are the situations in which type-II pair crystallography methods are insensitive because of the tiny number of ghosts. Moreover, in the flat cases, our method should be more sensitive than the type-I pair (or, in general, n-tuplet) methods because of its multifilter construction and its independence from n.
Key words: cosmology: theory / large-scale structure of Universe
© ESO, 2011
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