An improved cosmic crystallography method to detect holonomies in flat spaces

Abstract

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 \emph{separation, vectorial condition}, and \emph{lifetime of objects} extract these quadruplets. Each object $P_i$ is assigned an integer $s_i$, which is the number of candidate quadruplets including $P_i$ as their members. Then an additional device of $s_i$-histogram is used to extract topological ghosts, which tend to have high values of $s_i$. 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 $n$-th 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 $\Lambda$-CDM universes whose typical sizes correspond to $z\sim 5$. 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 $n$.}

12 pages, 8 figures, accepted for publication in A&A (2011)

References in corpus (22)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• The Sloan Digital Sky Survey Quasar Catalog V. Seventh Data Release
• Cosmic Topology
• Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background
• Circles in the Sky: Finding Topology with the Microwave Background Radiation
• Constraining the Topology of the Universe
• A Hint of Poincaré Dodecahedral Topology in the WMAP First Year Sky Map
• The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps
• Cosmic microwave background anisotropies in multi-connected flat spaces
• Extending the WMAP Bound on the Size of the Universe
• Do we Live in a "Small Universe"?
• On Determining the Topology of the Observable Universe via 3-D Quasar Positions
• Cosmic microwave background constraints on multi-connected spherical spaces
• A test of the Poincare dodecahedral space topology hypothesis with the WMAP CMB data
• The circles-in-the-sky signature for three spherical universes
• A spatial correlation analysis for a toroidal universe
• Circles-in-the-sky searches and observable cosmic topology in a flat Universe
• Poincare dodecahedral space parameter estimates
• Cosmic Crystallography with a Pullback
• On the suspected timing error in WMAP map-making
• Cosmic crystallography using short-lived objects - active galactic nuclei
• Cosmic microwave anisotropies in an inhomogeneous compact flat universe

Cited by in corpus (22)

• Planck 2013 results. XXVI. Background geometry and topology of the Universe
• Planck 2015 results. XVIII. Background geometry & topology
• The Status of Cosmic Topology after Planck Data
• Promise of Future Searches for Cosmic Topology
• A search for cosmic topology in the final WMAP data
• Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches
• Electromagnetic vacuum fluctuations and topologically induced motion of a charged particle
• Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds
• Deep redshift topological lensing: strategies for the T^3 candidate
• The Hantzsche-Wendt Manifold in Cosmic Topology
• Cosmic Topology of Polyhedral Double-Action Manifolds
• A search for nontoroidal topological lensing in the Sloan Digital Sky Survey quasar catalog
• Gravitational potential in spherical topologies
• Cosmic Topology : Twenty Years After
• Probing spatial orientability of Friedmann--Robertson--Walker spatially flat spacetime
• Inquiring electromagnetic quantum fluctuations about the orientability of space
• Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes
• A spatial-correlation analysis of the cubic 3-torus topology based on the Planck 2013 data
• On the possibility for constraining cosmic topology from the celestial distribution of astronomical objects
• Cosmic topology. Part IIIb. Eigenmodes and correlation matrices of spin-2 perturbations in orientable Euclidean manifolds
• A coordinate-independent technique for detecting globally inhomogeneous flat topologies
• Probing time orientability of spacetime