The luminosity-volume method : Derivation of the cosmological number density in depth from V/Vm distribution [Number density in depth from luminosity-volume]

The classical cosmological V/Vm-test is introduced and elaborated. Use of the differential distribution p(V/Vm) of the V/Vm-variable rather than just the mean <V/Vm> leads directly to the cosmological number density without any need for assumptions about the cosmological evolution of the underlying (quasar) population. Calculation of this number density n(z) from p(V/Vm) is illustrated using the best sample that was available in 1981, when this method was developed. This sample of 76 quasars is clearly too small for any meaningful results. The method will be later applied to a much larger cosmological sample to infer the cosmological number density n(z) as a function of the depth z. Keywords: V/Vm . luminosity volume . cosmological number density . V/Vm distribution

💡 Research Summary

The paper revisits the classic V/Vm test—a statistical tool used in observational cosmology to assess whether a population of astronomical objects (typically quasars, galaxies, or radio sources) is uniformly distributed in space. In its traditional form the test computes, for each object, the ratio of the comoving volume V actually occupied (derived from its redshift) to the maximum comoving volume Vm within which the object could still be detected given the survey’s flux limit. If the underlying population is homogeneous and non‑evolving, the distribution of V/Vm should be uniform on the interval