1999A&A...348....8R

If the assumption that physical space has a trivial topology is dropped, then the Universe may be described by a multiply connected Friedmann-Lemaitre model on a sub-horizon scale. Specific candidates for the multiply connected space manifold have already been suggested. How precisely would a significant detection of multiple topological images of a single object, or a region on the cosmic microwave background, (due to photons arriving at the observer by multiple paths which have crossed the Universe in different directions), constrain the values of the curvature parameters Ω₀ and λ₀? The way that the constraints on Ω₀ and λ₀ depend on the redshifts of multiple topological images and on their radial and tangential separations is presented and calculated. The tangential separations give the tighter constraints: multiple topological images of known types of astrophysical objects at redshifts z≲3 would imply values of Ω₀ and λ₀ preciser than ∼1% and ∼10% respectively. Cosmic microwave background `spots' identified with lower redshift objects by the Planck or MAP satellites would provide similar precision. This method is purely geometrical: no dynamical assumptions (such as the virial theorem) are required and the constraints are independent of the Hubble constant, H₀.