Constraints on the global topology and size of the universe from the cosmic microwave background

We study the possibility that the universe is flat, but with one or more space directions compactified. Using the seven-year WMAP data, we constrain the size of the compact dimension to be L/L0 ≥ 1.27,0.97,0.57 at 95% confidence for the case of three, two and one compactified dimension, respectively, where L0 = 14.4 Gpc is the distance to the last scattering surface. We find a statistically significant signal for a compact universe, and the best-fit spacetime is a universe with two compact directions of size L/L0 = 1.9, with the non-compact direction pointing in a direction close to the velocity of the Local Group