Angular diameters as a probe of a cosmological constant and Omega

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 q sub 0 = 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, Lambda, in a flat universe. The sensitivity to a nonzero Lambda in a flat universe is compared to the sensitivity to q sub 0 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 Omega 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 percent in source size for z of less than 2 can completely alter the results, and so must be convincingly ruled out if this technique is to provide a new tool for cosmology.