The topology of the Universe can leave an imprint on the cosmic microwave background (CMB) radiation. Clues to the shape of our Universe can be found by searching the CMB for matching circles of temperature patterns. A full sky search of the CMB, mapped extremely accurately by NASA’s WMAP satellite, returned no detection of such matching circles and placed a lower bound on the size of the Universe at 24 Gpc. This lower bound can be extended by optimally filtering the WMAP power spectrum. More stringent bounds can be placed on specific candidate topologies by using a combination statistic. We use optimal filtering and the combination statistic to rule out the suggestion that we live in a Poincaré dodecahedral space.

• Received 17 May 2006

DOI:https://doi.org/10.1103/PhysRevD.75.084034