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

Although the cubic {ital T}{sup 3} {open_quote}{open_quote}small universe{close_quote}{close_quote} 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 {ital T}{sup 3} {open_quote}{open_quote}small universe{close_quote}{close_quote} with one or two of its dimensions significantly smaller than the present horizon (which we refer to as {ital T}{sup 1} and {ital T}{sup 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 place a lower limit on the smallest cell size for {ital T}{sup 1} and {ital T}{sup 2} models of 3000 {ital h}{sup {minus}1} Mpc, at 95{percent} confidence, for a scale-invariant power spectrum ({ital n}=1). These results imply that {ital all} toroidal universes (cubes and rectangles) are ruled out as interesting cosmological models. {copyright} {ital 1996 The American Astronomical Society.}