Relativistic Cosmology Number Densities and the Luminosity Function
  This paper studies the connection between the relativistic number density of
galaxies down the past light cone in a Friedmann-Lemaitre-Robertson-Walker
spacetime with non-vanishing cosmological constant and the galaxy luminosity
function (LF) data. It extends the redshift range of previous results presented
in Albani et al. (2007:astro-ph/0611032) where the galaxy distribution was
studied out to z=1. Observational inhomogeneities were detected at this range.
This research also searches for LF evolution in the context of the framework
advanced by Ribeiro and Stoeger (2003:astro-ph/0304094), further developing the
theory linking relativistic cosmology theory and LF data. Selection functions
are obtained using the Schechter parameters and redshift parametrization of the
galaxy luminosity functions obtained from an I-band selected dataset of the
FORS Deep Field galaxy survey in the redshift range 0.5<z<5.0 for its blue
bands and 0.75<z<3.0 for its red ones. Differential number counts, densities
and other related observables are obtained, and then used with the calculated
selection functions to study the empirical radial distribution of the galaxies
in a fully relativistic framework. The redshift range of the dataset used in
this work, which is up to five times larger than the one used in previous
studies, shows an increased relevance of the relativistic effects of expansion
when compared to the evolution of the LF at the higher redshifts. The results
also agree with the preliminary ones presented in Albani et al.
(2007:astro-ph/0611032), suggesting a power-law behavior of relativistic
densities at high redshifts when they are defined in terms of the luminosity
distance.
