Constraints on the topology of the Universe derived from the 7-yr WMAP data

We impose constraints on the topology of the Universe determined from a search for matched circles in the temperature anisotropy patterns of the 7-yr Wilkinson Microwave Anisotropy Probe (WMAP) data. We pay special attention to the sensitivity of the method to residual foreground contamination of the sky maps and show that for a full-sky estimate of the CMB signal (the Internal Linear Combination map) such residuals introduce a non-negligible effect on the statistics of matched circles. In order to reduce this effect, we perform the analysis on maps for which the most contaminated regions have been removed. A search for pairs of matched back-to-back circles in the higher resolution WMAP W-band map allows tighter constraints to be imposed on topology. Our results rule out universes with topologies that predict pairs of such circles with radii larger than αmin≈ 10°. This places a lower bound on the size of the fundamental domain for a flat universe of about 27.9 Gpc. This bound is close to the upper limit on the size of Universe possible to be detected by the method of matched circles, i.e. the diameter of the observable Universe is 28.3 Gpc.