Angular Diameters as a Probe of a Cosmological Constant and $Ω$

Abstract

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, depends sensitively on the value of the cosmological constant, $Λ$, in a flat universe. The redshift of an observed minimum and the asymptotic slope can in principle provide strong constraints on $Λ$. The sensitivity to a non-zero cosmological constant in a flat universe is compared to the sensitivity to $q_0$ in an open universe without a cosmological constant, and to inherent ambiguities due to uncertainties in distance measures and the possible effects of evolution. If evolutionary uncertainties can be overcome, the reported observations of the angular diameter of compact radio jets as a function of redshift, which appear to exhibit such a minimum, could provide the strongest available limit on the cosmological constant in a flat universe, and on $Ω$ in an open universe.