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

TL;DR

This paper introduces a method to derive the cosmological number density as a function of depth using the V/Vm distribution, avoiding assumptions about population evolution, and demonstrates its application with a small quasar sample.

Contribution

The paper presents a novel approach using the differential V/Vm distribution to directly calculate cosmological number density without evolution assumptions.

Findings

Method successfully applied to a small quasar sample.

Potential for application to larger datasets for cosmological insights.

Provides a new tool for analyzing the spatial distribution of quasars.

Abstract

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