MEASURING THE TOPOLOGY OF THE UNIVERSE

Observations of microwave background fluctuations can yield informatio n not only about the geometry of the universe but potentially about th e topology of the universe. If the universe is negatively curved, then the characteristic scale for the topology of the universe is the curv ature radius. Thus, if we are seeing the effects of the geometry of th e universe, we can hope to soon see signatures of the topology of the universe. The cleanest signature of the topology of the universe is wr itten on the microwave sky: There should be thousands of pairs of matc hed circles. These circles can be used to determine the precise topolo gy and volume of the universe. Because we see hundreds of slices throu gh the fundamental domain of the universe, we can use the microwave ob servations to reconstruct the initial conditions of the entire univers e on the scale of a few megaparsecs.