Constraints on the Topology of the Universe from the Wilkinson Microwave Anisotropy Probe First-Year Sky Maps

We compute the covariance expected between the spherical harmonic coefficients a sub(lm) of the cosmic microwave temperature anisotropy if the universe had a compact topology. For a fundamental cell size smaller than the distance to the decoupling surface, off-diagonal components carry more information than the diagonal components (the power spectrum). We use a maximum likelihood analysis to compare the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data to models with a cubic topology. The data are compatible with finite flat topologies with fundamental domain L > 1.2 times the distance to the decoupling surface at a 95% confidence level. The WMAP data show reduced power at the quadrupole and octopole, but they do not show the correlations expected for a compact topology and are indistinguishable from infinite models.