On Determining the Topology of the Observable Universe via 3-D Quasar Positions

Abstract

Hot big bang cosmology says nothing about the topology of the Universe. A topology-independent algorithm is presented which is complementary to that of Lehoucq et al. 1996 and which searches for evidence of multi-connectedness using catalogues of astrophysically observed objects. The basis of this algorithm is simply to search for a quintuplet of quasars (over a region of a few hundred comoving Mpc) which can be seen in two different parts of our past time cone, allowing for a translation, an arbitrary rotation and possibly a reflection. This algorithm is demonstrated by application to the distribution of quasars between redshifts of $z=1$ and $z\approx 4,$ i.e., at a comoving distance from the observer $1700 h^{-1}\mbox{\rm Mpc} \ltapprox d \ltapprox 3300 h^{-1}\mbox{\rm Mpc}.$ Two pairs of isometric quintuplets separated by more than {$300$\hMpc} are found. This is consistent with the number expected from Monte Carlo simulations in a simply connected Universe if the detailed anisotropy of sky coverage by the individual quasar surveys is taken into account. The linear transformation in (flat) comoving space from one quintuplet to another requires translations of {$353$\hMpc} and {4922\hMpc} respectively, plus a reflection in the former case, and plus both a rotation and a reflection in the latter. Since reflections are required, if these two matches were due to multi-connectedness, then the Universe would be non-orientable.

6 pages, including Figures 2,3; self-extracting uuencoded \LaTeX plus postscript; Figure 1 available at ftp://www.iap.fr/pub/from_users/roukema/LSSd.ps.gz ; full article available at ftp://www.iap.fr/pub/from_users/roukema/qsotop.ps.gz as gzipped concatenation of postscript files (340kb)

Cited by in corpus (34)

• Topology and the Cosmic Microwave Background
• Planck 2013 results. XXVI. Background geometry and topology of the Universe
• A Hint of Poincaré Dodecahedral Topology in the WMAP First Year Sky Map
• Planck 2015 results. XVIII. Background geometry & topology
• Detectability of Cosmic Topology in Almost Flat Universes
• Are Small Hyperbolic Universes Observationally Detectable?
• A Topological Signature in Cosmic Topology
• An improved cosmic crystallography method to detect holonomies in flat spaces
• On Closed Einstein-de Sitter Universes
• Promise of Future Searches for Cosmic Topology
• COBE and Global Topology: An Example of the Application of the Identified Circles Principle
• A Counterexample to Claimed COBE Constraints on Compact Toroidal Universe Models
• Constraints on the Detectability of Cosmic Topology from Observational Uncertainties
• Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches
• Detectability of Cosmic Topology in Flat Universes
• Three-dimensional Topology-Independent Methods to Look for Global Topology
• Radiation Damping in FRW Space-times with Different Topologies
• Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds
• Ghosts of the Milky Way: a search for topology in new quasar catalogues
• Deep redshift topological lensing: strategies for the T^3 candidate
• Cosmic crystallography using short-lived objects - active galactic nuclei
• The size of the Universe according to the Poincare dodecahedral space hypothesis
• Transverse Galaxy Velocities from Multiple Topological Images
• A search for nontoroidal topological lensing in the Sloan Digital Sky Survey quasar catalog
• Can We See the Shape of the Universe?
• An Axisymmetric Object-Based Search for a Flat Compact Dimension
• Gravitational potential in spherical topologies
• Topology and Fragility in Cosmology
• How to Avoid the Ambiguity in Applying the Copernican Principle for Cosmic Topology: Take the Observational Approach
• A constraint on any topological lensing hypothesis in the spherical case: it must be a root of the identity
• Topology of the Universe: background and recent observational approaches
• On the possibility for constraining cosmic topology from the celestial distribution of astronomical objects
• Topology of space at sub-quark level and masses of quarks and leptons
• A coordinate-independent technique for detecting globally inhomogeneous flat topologies