Minimal Angular Size of Distant Sources in Open, ΛCDM, and Scalar Field Cosmologies

We propose a simple method for determining the redshift $z_{m}$ at which the angular size of an extragalactic source with fixed proper diameter takes its minimal value. A closed analytical expression, which is quite convenient for numerical evaluation is derived. The method is exemplified with the following FRW type expanding universes: the open matter dominated models ($\Omega_{\Lambda}= 0$), a critical density model with cosmological constant ($\Omega_{\Lambda} \neq 0$), and the class of scalar field cosmologies proposed by Ratra and Peebles. The influence of systematic evolutionary effects is briefly discussed.