Determining the shape of the Universe using discrete sources

Suppose we have identified three clusters of galaxies as being topological copies of the same object. How does this information constrain the possible models for the shape of our Universe? It is shown here that, if the Universe has flat spatial sections, these multiple images can be accommodated within any of the six classes of compact orientable 3-dimensional flat space forms. Moreover, the discovery of two more triples of multiple images in the neighbourhood of the first one, would allow the determination of the topology of the Universe, and in most cases the determination of its size.Comment: 11 pages, no figure

Constraints on the Detectability of Cosmic Topology from Observational Uncertainties

Recent observational results suggest that our universe is nearly flat and well modelled within a $\Lambda$CDM framework. The observed values of $\Omega_{m}$ and $\Omega_{\Lambda}$ inevitably involve uncertainties. Motivated by this, we make a systematic study of the necessary and sufficient conditions for undetectability as well as detectability (in principle) of cosmic topology (using pattern repetition) in presence of such uncertainties. We do this by developing two complementary methods to determine detectability for nearly flat universes. Using the first method we derive analytical conditions for undetectability for infinite redshift, the accuracy of which is then confirmed by the second method. Estimates based on WMAP data together with other measurements of the density parameters are used to illustrate both methods, which are shown to provide very similar results for high redshifts.Comment: 16 pages, 1 figure, LaTeX2