Abstract
The luminosity–volume test for a complete sample of quasi-stellar objects which consists of all those brighter than prescribed limiting radio and optical flux densities, is investigated. The best available sample of QSOs which fulfil these completeness criteria, that discussed by Schmidt, is used in our analysis. We show that: (i) The luminosity–volume test does not depend upon the association of a particular redshift with a particular QSO—all that is important is the range of redshifts of the QSOs; (ii) The luminosity-volume test and the counts of radio sources and of QSOS are very closely related. The two tests are not independent methods of investigating the evolution of QSOs over cosmological time-scales; (iii) ‘Luminosity ’ and ‘density’ evolution hypotheses are indistinguishable from the present QSO data and in principle it is very doubtful if they can be distinguished; (iv) The counts of radio sources are inconsistent with the predictions of realistic Lemaitre models in which the distribution of sources is assumed uniform; and (v) The luminosity–volume test for QSOs in Lemaitre world models is not consistent with a uniform distribution of sources, in agreement with (iv).
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