Cosmological number density in depth from V/Vm distribution

TL;DR

This paper discusses a method to derive the cosmological number density n(z) from the distribution p(V/Vm) of volume ratios, illustrated with a small quasar sample, emphasizing the potential of the approach.

Contribution

It introduces a novel use of the V/Vm distribution to directly calculate cosmological number density, expanding beyond the traditional mean-based methods.

Findings

Demonstrated calculation of n(z) from p(V/Vm) using a 1981 quasar sample

Highlighted the potential of the method despite small sample size

Suggested the approach could be applied to larger datasets for meaningful results

Abstract

Using distribution p(V/Vm) of V/Vm rather than just mean <V/Vm> in V/Vm-test leads directly to cosmological number density n(z). Calculation of n(z) from p(V/Vm) is illustrated using best sample (of 76 quasars) available in 1981, when method was developed. This is only illustrative, sample being too small for any meaningful results. Keywords: V/Vm . luminosity volume . cosmological number density . V/Vm distribution