Constraints on the topology of the Universe: Extension to general geometries
Abstract
We present an update to the search for a nontrivial topology of the Universe by searching for matching circle pairs in the cosmic microwave background [N. J. Cornish Phys. Rev. Lett. 92, 201 302 (2004)] using the WMAP 7year data release. We extend the existing bounds to encompass a wider range of possible topologies by searching for matching circle pairs with opening angles 10°≤α≤90° and separation angles 11°≤θ≤180°. The extended search reveals two small anomalous regions in the cosmic microwave background sky. Numerous pairs of wellmatched circles are found where both circles pass through one or the other of those regions. As this is not the signature of any known manifold, but is a likely consequence of contamination in those sky regions, we repeat the search excluding circle pairs where both pass through either of the two regions. We then find no statistically significant pairs of matched circles, and so no hints of a nontrivial topology. The absence of matched circles increases the lower limit on the length of the shortest closed null geodesic that selfintersects at our location in the Universe (equivalently the injectivity radius at our location) to 98.5% of the diameter of the last scattering surface or approximately 26 Gpc. It extends the limit to any manifolds in which the intersecting arcs of said geodesic form an angle greater than 10°.
 Publication:

Physical Review D
 Pub Date:
 October 2012
 DOI:
 10.1103/PhysRevD.86.083526
 arXiv:
 arXiv:1206.2939
 Bibcode:
 2012PhRvD..86h3526V
 Keywords:

 98.80.k;
 04.20.Gz;
 98.70.Vc;
 98.80.Es;
 Cosmology;
 Spacetime topology causal structure spinor structure;
 Background radiations;
 Observational cosmology;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 11 pages, 11 figures