Minimal Angular Size of Distant Sources in Open, $Λ$CDM, and Scalar Field Cosmologies

Abstract

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 ($Ω_Λ= 0$), a critical density model with cosmological constant ($Ω_Λ \neq 0$), and the class of scalar field cosmologies proposed by Ratra and Peebles. The influence of systematic evolutionary effects is briefly discussed.