Differential density statistics of the galaxy distribution and the luminosity function

This paper uses data obtained from the galaxy luminosity function (LF) to calculate two types of radial number density statistics of the galaxy distribution as discussed in Ribeiro, namely, the differential density gamma and the integral differential density gamma*. By applying the theory advanced by Ribeiro & Stoeger, which connects the relativistic cosmology number counts with the astronomically derived LF, the differential number counts dN/dz are extracted from the LF and used to calculate both gamma and gamma* with various cosmological distance definitions, namely, area distance, luminosity distance, galaxy area distance, and redshift distance. LF data are taken from the CNOC2 galaxy redshift survey, and gamma and gamma* are calculated for two cosmological models: Einstein-de Sitter and an Omega(m0) = 0.3, Omega(Lambda 0) = 0.7 standard cosmology. The results confirm the strong dependency of both statistics on the distance definition, as predicted in Ribeiro, as well as showing that plots of gamma and gamma* against the luminosity and redshift distances indicate that the CNOC2 galaxy distribution follows a power-law pattern for redshifts higher than 0.1. These findings support Ribeiro's theoretical proposition that using different cosmological distance measures in statistical analyses of galaxy surveys can lead to significant ambiguity in drawing conclusions about the behavior of the observed large-scale distribution of galaxies.