The Power Spectrum of Cosmological Number Densities
  We study the cosmological power spectra (PS) of the differential and integral
galaxy volume number densities $\gamma_i$ and $\gamma_i^{*}$, constructed with
the cosmological distances $d_i$ $(i=A,G,L,Z)$, where $d_A$ is the angular
diameter distance, $d_G$ is the galaxy area distance, $d_L$ is the luminosity
distance and $d_z$ is the redshift distance. Theoretical and observational
quantities were obtained in the FLRW spacetime with a non-vanishing $\Lambda$.
The radial correlation $\Xi_i$, as defined in the context of these densities,
is discussed in the wave number domain. All observational quantities were
computed using luminosity function (LF) data obtained from the FORS Deep Field
galaxy survey. The theoretical and observational PS of $\gamma_i$,
$\gamma_i^{\ast}$, $\Xi_i$ and $\gamma_i / \gamma_i^\ast$ were calculated by
performing Fourier transforms on these densities previously derived by
Iribarrem et al. (2012) from the observed values $\gamma_{obs}$ and
${\gamma^\ast}_{obs}$ obtained using the galactic absolute magnitudes and
galaxy LF Schechter's parameters presented in Gabasch et al. (2004, 2006) in
the range $0.5 \le z \le5.0$. The results show similar behavior of the PS
obtained from $\gamma$ and $\gamma^{\ast}$ using $d_L$, $d_z$ and $d_G$ as
distance measures. The PS of the densities defined with $d_A$ have a different
and inconclusive behavior, as this cosmological distance reaches a maximum at
$z\approx 1.6$ in the adopted cosmology. For the other distances, our results
suggest that the PS of ${\gamma_i}_{obs}$, ${\gamma^\ast_i}_{obs}$ and
${\gamma_i / \gamma^{\ast}_i}_{obs}$ have a general behavior approximately
similar to the PS obtained with the galaxy two-point correlation function and,
by being sample size independent, they may be considered as alternative
analytical tools to study the galaxy distribution.
