Limits on the Detectability of Cosmic Topology in Hyperbolic Universes

Abstract

We reexamine the possibility of the detection of the cosmic topology in nearly flat hyperbolic Friedmann-Lemaitre-Robertson-Walker (FLRW) universes by using patterns repetition. We update and extend our recent results in two important ways: by employing recent observational constraints on the cosmological density parameters as well as the recent mathematical results concerning small hyperbolic 3-manifolds. This produces new bounds with consequences for the detectability of the cosmic topology. In addition to obtaining new bounds, we also give a concrete example of the sensitive dependence of detectability of cosmic topology on the uncertainties in the observational values of the density parameters.

arXiv comment10 pages, 2 figures, LaTeX2e. To appear in Int. J. Mod. Phys. A (2002). Contribution to the Fifth Alexander Friedmann International Seminar on Gravitation and Cosmology

References in corpus (11)

• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• The High-Z Supernova Search: Measuring Cosmic Deceleration and Global Cur vature of the Universe Using Type Ia Supernovae
• Cosmology from Maxima-1, Boomerang and COBE/DMR CMB Observations
• Topology and the Cosmic Microwave Background
• Topological Lensing in Spherical Spaces
• Detectability of Cosmic Topology in Almost Flat Universes
• Are Small Hyperbolic Universes Observationally Detectable?
• Volume change under drilling
• The Cosmological Constant and Quintessence from a Correlation Function Comoving Fine Feature in the 2dF Quasar Redshift Survey
• The Quintessential CMB, Past & Future

Cited by in corpus (22)

• WMAP data and the curvature of space
• Simulating Cosmic Microwave Background maps in multi-connected spaces
• Generalized Chaplygin gas model, supernovae and cosmic topology
• Cosmic microwave background constraints on multi-connected spherical spaces
• Circles-in-the-sky searches and observable cosmic topology in a flat Universe
• Detecting topology in a nearly flat hyperbolic universe
• A note on the large-angle anisotropies in the WMAP cut-sky maps
• What do very nearly flat detectable cosmic topologies look like?
• 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
• Electromagnetic vacuum fluctuations and topologically induced motion of a charged particle
• Relativistic Effects of our Galaxy's Motion on Circles-in-the-sky
• Circles-in-the-sky searches and observable cosmic topology in the inflationary limit
• What can the detection of a single pair of circles-in-the-sky tell us about the geometry and topology of the Universe ?
• Limits of the circles-in-the-sky searches in the determination of cosmic topology of nearly flat universes
• Inquiring electromagnetic quantum fluctuations about the orientability of space
• Horizon Complementarity and Casimir Violations of the Null Energy Condition
• Non-Gaussianity in the HILC foreground-reduced three-year WMAP CMB map
• Determining the shape of the Universe using discrete sources
• Decoupling Inflation From the String Scale