Can the Lack of Symmetry in the COBE DMR Maps Constrain the Topology of the Universe?

Although the cubic T3 "small universe" has been ruled out by COBE Differential Microwave Radiometer (DMR) results as an interesting cosmological model, we still have the possibility of living in a universe with a more anisotropic topology, such as a rectangular T3 "small universe" with one or two of its dimensions significantly smaller than the present horizon (which we refer to as T1 and T2 models, respectively). In order to rule out these anisotropic topologies as well, we apply a new data analysis method that searches for the specific kind of symmetries that these models should produce. We find that the 4 year COBE DMR data place a lower limit on the smallest cell size for T1 and T2 models of 3000 h-1 Mpc, at 95% confidence, for a scale-invariant power spectrum (n = 1). These results imply that all toroidal universes (cubes and rectangles) are ruled out as interesting cosmological models.