A Topological Signature in Cosmic Topology

Abstract

Two procedures for obtaining (extracting and constructing) the topological signature of any multiply connected Robertson-Walker (RW) universe are presented. It is shown through computer-aided simulations that both approaches give rise to the same topological signature for a multiply connected flat RW universe. The strength of these approaches is illustrated by extracting the topological signatures of a flat ($k=0$), an elliptic ($k=1$), and a hyperbolic ($k=-1$) multiply connected RW universes. We also show how separated contributions of the covering isometries add up to form the topological signature of a RW flat universe. There emerges from our theoretical results and simulations that the topological signature arises (in the mean) even when there are just a few images for each object. It is also shown that the mean pair separation histogram technique works, and that it is a suitable approach for studying the topological signatures of RW universes as well as the role of non-translational isometries.

27 pages, 7 figures, LaTeX2e. Inserted: clarifying details, a connection with CCP method, new references. To appear in Class. Quantum Grav. (2001) in the present form

References in corpus (9)

• First Estimations of Cosmological Parameters From BOOMERANG
• CMB Anisotropy in Compact Hyperbolic Universes I: Computing Correlation Functions
• CMB Anisotropy in Compact Hyperbolic Universes II: COBE Maps and Limits
• Spikes in Cosmic Crystallography II: Topological Signature of Compact Flat Universes
• The Fluctuations of the Cosmic Microwave Background for a Compact Hyperbolic Universe
• A Counterexample to Claimed COBE Constraints on Compact Toroidal Universe Models
• COBE Constraints on a Compact Toroidal Low-density Universe
• Limits of crystallographic methods for detecting space topology
• Observational Approaches to the Topology of the Universe

Cited by in corpus (26)

• Topology and the Cosmic Microwave Background
• A Hint of Poincaré Dodecahedral Topology in the WMAP First Year Sky Map
• Topological Lensing in Spherical Spaces
• Mapping the large-scale anisotropy in the WMAP data
• Generalized Chaplygin gas model, supernovae and cosmic topology
• Detecting Topology in a Nearly Flat Spherical Universe
• Detectability of Cosmic Topology in Almost Flat Universes
• Are Small Hyperbolic Universes Observationally Detectable?
• Spikes in Cosmic Crystallography II: Topological Signature of Compact Flat Universes
• A note on the large-angle anisotropies in the WMAP cut-sky maps
• Constraints on the Detectability of Cosmic Topology from Observational Uncertainties
• Observational constraints on modified gravity models and the Poincaré dodecahedral topology
• Detectability of Cosmic Topology in Flat Universes
• Topological signatures in CMB temperature anisotropy maps
• Distinguishing Marks of Simply-connected Universes
• Detectability of Cosmic Topology in Generalized Chaplygin Gas Models
• A method to search for topological signatures in the angular distribution of cosmic objects
• Inquiring electromagnetic quantum fluctuations about the orientability of space
• Cosmic crystallography: the euclidean isometries
• Cosmic crystallography in a circle
• Constraints on the cosmological density parameters and cosmic topology
• Cosmic crystallography: the hyperbolic isometries
• Probing time orientability of spacetime
• Distances in plane membranes
• Topological Expansion, Study and Applications
• Separations inside a cube