Universes with two degrees of freedom (Q o 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 (Q o -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.
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Jackson et al. (1996) studied this question.