On universes with outsides and the angular-size/redshift diagram for milliarcsecond radio-sources

Abstract

Universes with two degrees of freedom (Qo and Ao) are examined in the light of Kellerman's compilation of angular-size/redshift data for ultracompact radio sources. We find that low-density (Qo 0.2) models which are violently decelerating and have a large negative cosmological constant (qo Ao 3) fit the data very well, as well as the canonical cold dark matter (CDM) universe, and very much better than the spatially flat accelerating case; if Q o::;;O.2, then 95 per cent confidence limits are 3.8 ::;;Ao::;; 1.1, the lower limit being fixed by Holo ~ 0.56. The significant qualitative feature of the ()-z curve in this context is asymptotic flatness (in the limit Q o ...... 0, Ao # 0), rather than a pronounced minimum angular size. We give a mathematically rigorous argument, based upon the focusing of congruences of null geodesics, which shows that this feature is a singular property of vacuum-dominated universes.