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 ΛCDM framework. The observed values of Ωm and ΩΛ inevitably involve uncertainties. Motivated by this, we conduct a systematic study of the necessary and sufficient conditions for undetectability and detectability (in principle) of cosmic topology (using pattern repetition) in the 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