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-Lema^itre 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 two fifths of the horizon diameter. To show that this claim is misleading, a simple $T^2 \times R$ 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.