Eur. Phys. J. Plus (2022) 137: 942
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

^b mbr@if.ufrj.br

Received: 1 April 2022
Accepted: 7 August 2022
Published online: 20 August 2022

Abstract

This paper studies the cosmological power spectrum (PS) of the differential and integral galaxy volume number densities, respectively, ${\gamma }_i$ and ${\gamma }_i^{\ast }$, 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 Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime with a non-vanishing cosmological constant. The radial correlation ${\mathrm{\Xi }}_i$, 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 ${\gamma }_i$, ${\gamma }_i^{\ast }$, ${\mathrm{\Xi }}_i$ and the ratio ${\gamma }_i/{\gamma }_i^{\ast }$ 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 ${[\gamma ]}_{\mathrm{obs}}$ and ${[{\gamma }^{\ast }]}_{\mathrm{obs}}$ 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 $0.5\le z\le 5.0$ for its blue bands and $0.75\le z\le 3.0$ for its red ones. The results show similar behavior of the power spectra 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 because this cosmological distance reaches a maximum at $z\approx 1.6$ in the adopted cosmological model. For the other distances, our results suggest that the PS of ${[{\gamma }_i]}_{\mathrm{obs}}$, ${[{\gamma }_i^{\ast }]}_{\mathrm{obs}}$ and ${[{\gamma }_i/{\gamma }_i^{\ast }]}_{\mathrm{obs}}$ 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.