What can the detection of a single pair of circles-in-the-sky tell us about the geometry and topology of the Universe ?

Abstract

In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations --- the so-called circles-in-the-sky. Searches undertaken for nearly antipodal pairs of such circles in cosmic microwave background maps have so far been unsuccessful. Previously we had shown that the negative outcome of such searches, if confirmed, should in principle be sufficient to exclude a detectable non-trivial spatial topology for most observers in very nearly flat ($0<\mid {\Omega }_{\text{tot}}-1\mid \lesssim 10^{-5}$) (curved) universes. More recently, however, we have shown that this picture is fundamentally changed if the universe turns out to be {\it exactly} flat. In this case there are many potential pairs of circles with large deviations from antipodicity that have not yet been probed by existing searches. Here we study under what conditions the detection of a single pair of circles-in-the-sky can be used to uniquely specify the topology and the geometry of the spatial section of the Universe. We show that from the detection of a \emph{single} pair of matching circles one can infer whether the spatial geometry is flat or not, and if so we show how to determine the topology (apart from one case) of the Universe using this information. An important additional outcome of our results is that the dimensionality of the circles-in-the-sky parameter space that needs to be spanned in searches for matching pair of circles is reduced from six to five degrees of freedom, with a significant reduction in the necessary computational time.

6 pages, 2 figures, 1 table. V2: Version to appear in Phys. Rev. D (Oct.,2011). Minor changes, references added. V3:Version published in Phys.Rev.D. Typos corrected, presentation of a point improved

References in corpus (8)

• Extending the WMAP Bound on the Size of the Universe
• Do we Live in a "Small Universe"?
• A spatial correlation analysis for a toroidal universe
• Circles-in-the-sky searches and observable cosmic topology in a flat Universe
• The spectral action and cosmic topology
• On the detectability of non-trivial topologies
• Cosmic microwave anisotropies in an inhomogeneous compact flat universe
• On the possibility for constraining cosmic topology from the celestial distribution of astronomical objects

Cited by in corpus (9)

• Planck 2013 results. XXVI. Background geometry and topology of the Universe
• Some statistical remarks on the Giant GRB Ring
• A search for cosmic topology in the final WMAP data
• The Hantzsche-Wendt Manifold in Cosmic Topology
• Limits of the circles-in-the-sky searches in the determination of cosmic topology of nearly flat universes
• Cosmic Topology of Polyhedral Double-Action Manifolds
• Orbifold Line Topology and the Cosmic Microwave Background
• A spatial-correlation analysis of the cubic 3-torus topology based on the Planck 2013 data
• Effect of the cubic torus topology on cosmological perturbations