Angular diameters as a probe of a cosmological constant and Ω

The lensing effect of curved space, which can cause the angular diameter of a fixed reference length seen on the sky to reach a minimum and then increase with redshift, has recently been claimed to provide evidence, using compact radio sources, for a q₀ = 1/2 expansion. We show here that this relation, in particular the position of the observed minimum, depends sensitively on the value of the cosmological constant, Λ, in a flat universe. The sensitivity to a nonzero Λ in a flat universe is compared to the sensitivity to q₀ in an open universe without a cosmological constant. The reported results could provide the strongest available limit on the cosmological constant in a flat universe (and on Ω in an open universe) and so we explore how uncertainties in distance measures and evolution of the sources can affect the results. Evolution of less than 30% in source size for z ≤ 2 can completely alter the results, and so must be convincingly ruled out if this technique is to provide a new tool for cosmology.