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

Abstract

Although the cubic T^3 small has been ruled out by COBE/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 T^3 small with one or two of its dimensions significantly smaller than the present horizon (which we refer to as T^1- and T^2-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 set a lower limit on the smallest cell size for T^1- and T^2-models of 3000h^{-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.