https://doi.org/10.1140/epjp/s13360-022-03168-7
Regular Article
The power spectrum of cosmological number densities
1
Valongo Observatory, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
2
Department of Astronomy, Observatório Nacional, Rio de Janeiro, Brazil
3
Physics Institute, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
4
Vatican Observatory Research Group, Steward Observatory, University of Arizona, Tucson, USA
Received:
1
April
2022
Accepted:
7
August
2022
Published online:
20
August
2022
This paper studies the cosmological power spectrum (PS) of the differential and integral galaxy volume number densities, respectively, 
and 
, constructed with the cosmological distances 
, where 
is the angular diameter distance, 
is the galaxy area distance, 
is the luminosity distance and 
is the redshift distance. Theoretical and observational quantities were obtained in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime with a non-vanishing cosmological constant. The radial correlation 
, a quantity defined in the context of these densities, is also discussed in the wave number domain. All observational quantities were computed using luminosity function (LF) data obtained from the FORS Deep Field (FDF) galaxy survey. The theoretical and observational power spectra of , , and the ratio 
were calculated by performing Fourier transforms on values of these densities which were previously derived by Iribarrem (Astron. Astrophys. 539:A112, 2012) from the observational values 
and 
obtained by using the galactic absolute magnitudes and Schechter’s parameters of the galaxy LF presented in Gabasch (Astron. Astrophys. 421:41–58, 2004; Astron. Astrophys. 448:101, 2006). These parameters were evaluated from a I-band selected dataset of the FDF in the redshift range 
for its blue bands and 
for its red ones. The results show similar behavior of the power spectra obtained from 
and 
using , and as distance measures. The PS of the densities defined with have a different and inconclusive behavior because this cosmological distance reaches a maximum at 
in the adopted cosmological model. For the other distances, our results suggest that the PS of 
, 
and 
has a general behavior approximately similar to the power spectra 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.
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