Constraints on the Topology of the Universe from the 2 Year COBE Data

The cosmic microwave background (CM B) is a unique probe of cosmological parameters and conditions. There is a connection between anisotropy in the CMB and the topology of the universe. Adopting a universe with the topology of a three-torus, or a universe where only harmonics of the fundamental mode are allowed, and using 2 years of C0BE/DMR data, we obtain constraints on the topology of the universe. Previous work constrained the topology using the slope information and the correlation function of the CMB. We obtain more accurate results by using all multipole moments, avoiding approximations by computing their full covariance matrix. We obtain the best fit for a cubic toroidal universe of scale 7200 h-1 Mpc for n = 1. The data set a lower limit on the cell size of 4320 h-1 Mpc at 95% confidence and 5880 h-1 Mpc at 68% confidence. These results show that the most probable cell size would be ∼1.2 times larger than the horizon scale, implying that the three-torus topology is no longer an interesting cosmological model.