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

Universes with two degrees of freedom (Omega(0) and Lambda(0)) are examined in the light of Kellerman's compilation of angular-size/redshift data for ultracompact radio sources. We find that low-density (Omega(0) similar to 0.2) models which are violently decelerating and have a large negative cosmological constant (q(0) similar to - Lambda(0) similar to 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 Omega(0) less than or equal to 0.2, then 95 per cent confidence limits are - 3.8 less than or equal to Lambda(0) less than or equal to - 1.1, the lower limit being fixed by H(0)t(0) greater than or equal to 0.56. The significant qualitative feature of the theta-z curve in this context is asymptotic flatness (in the limit Omega(0) -> 0, Lambda(0) not equal 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.