V V-MAX STATISTICS AND NEOCLASSICAL COSMOLOGICAL TESTS/

A new cosmological test is derived, based on the distribution of indiv idual V/V-max in a complete redshift-limited sample of distant objects . The fundamental assumption is that, in any range of absolute luminos ity, individual V/V-max are required to be uniformly spread over the [ 0: 1] range. Under the assumption of Pure Luminosity Evolution, this g ives rise to a natural partition of the sample into high luminosity: r edshift-limited and low luminosity magnitude-limited quasars. The beha vior of V/V-max versus evolution and cosmology differs substantially i n the two subsamples. This condition of uniformity is probed in any ab solute magnitude bin, allowing a likelihood function to be computed fr om the Kolmogorov-Smirnov probabilities of each bin. Monte-Carlo simul ations show that the test is mostly sensitive to the density parameter , but, under certain conditions, it also sets constraints on the space curvature and, to a lower extent, on the cosmological constant. Cross -tests between power law and exponential luminosity evolution laws are performed, showing that the functional form of luminosity evolution d oes not affect substantially the probabilities in the parameter space (Omega(0), Lambda). The efficiency of the test applied to two kinds of simulated quasar samples is examined: large number QSO sample, but li mited to redshifts z < 2.2 or smaller in QSO number, but with higher a redshift limit. Two observational strategies are compared; aimed at t he construction of such samples with the future instrumentation of the VLT. Finally, the test is applied to the UVX sample of Boyle et al. ( 1990). A low matter density, and a flat Universe without cosmological constant, are rejected: 0.2 < Omega < 0.8 within the 95% confidence le vel.