The Determination of the Evolutionary Properties of Quasars by Means of the Luminosity-Volume Test

A cosmological test suitable for sources with a large dispersion in luminosity, the luminosity-volume test, is described. Application to both the optical and radio data for quasars, assuming their redshifts to be cosmological, shows that none of the relativistic models can apply without some evolutionary factor that affects both radio and optical properties. Simple evolutionary hypotheses are tested, and it is found that only relatively empty models $$(4\pi G\rho_0\ll \text H_0\text{}^2)\text{ with}-1\leqslant q_0\leqslant0.5$$ are consistent with power-law luminosity-evolution, whereas all models are consistent with density-evolution. Evolutions with a negative exponential dependence on the scale-factor, which do not require a truncation of the evolving population at finite redshift to give a finite integrated background radiation, represent the data well. The test should be applicable to radio-galaxies when the data is more complete.