A counterexample to claimed COBE constraints on compact toroidal universe models

It has been suggested that if the Universe satisfies a flat, multiply connected, perturbed Friedmann-Lemaitre model, then cosmic microwave background data from the COBE satellite implies that the minimum size of the injectivity diameter (shortest closed spatial geodesic) must be larger than about a of the horizon diameter. To show that this claim is misleading, a simple T-2 X R universe model of injectivity diameter a quarter of this size, i.e. a tenth of the horizon diameter, is shown to be consistent with COBE four-year observational maps of the cosmic microwave background. This is done using the identified circles principle.