Do We Know the Geometry of the Universe?

Abstract

It is quite remarkable that seventy years after Hubble discovered the expansion of the Universe, we still have no idea in which of the three Friedmann-Robertson-Walker geometries we live. Most of the current literature has focussed on flat or open models. Here, we construct a viable model of the Universe which has closed geometry even though the nonrelativistic-matter density is less than critical. Furthermore, in this model, the cosmic microwave background could come from a causally-connected region at the antipode of the closed Universe. This model illustrates that the geometry of the Universe is unconstrained by current data. We discuss observations which may reliably determine the geometry of the Universe in the near future.