Derivation of the cosmological number density in depth from V/Vm distribution

TL;DR

This paper introduces a method using the differential V/Vm distribution to directly derive the cosmological number density n(z) without assuming population evolution, demonstrated on a small quasar sample with plans for larger future datasets.

Contribution

It presents a novel approach utilizing the V/Vm distribution to determine cosmological number density without evolution assumptions, applicable to larger samples.

Findings

Method demonstrated on 76 quasars, highlighting limitations due to small sample size.

Potential to infer n(z) from larger, more comprehensive datasets.

Provides a new tool for cosmological population studies.

Abstract

The classical cosmological V/Vm-test is introduced. 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