Signature for the Shape of the Universe

If the universe has a nontrivial shape (topology) the sky may show multiple correlated images of cosmic objects. These correlations can be couched in terms of distance correlations. We propose a statistical quantity which can be used to reveal the topological signature of any Robertson-Walker (RW) spacetime with nontrivial topology. We also show through computer-aided simulations how one can extract the topological signatures of flat, elliptic, and hyperbolic RW universes with nontrivial topology.