Relativistic cosmology number densities in void-Lemaitre-Tolman-Bondi models

Aims. The goal of this work is to compute the number density of far-IR selected galaxies in the comoving frame and along the past lightcone of observationally constrained Lemaitre-Tolman-Bondi giant void models and to compare those results with their standard model counterparts. Methods. We derived integral number densities and differential number densities using different cosmological distance definitions in the Lemaitre-Tolman-Bondi dust models. Then, we computed selection functions and consistency functions for the luminosity functions in the combined fields of the Herschel/PACS evolutionary probe (PEP) survey in both standard and void cosmologies, from which we derived the observed values of the above-mentioned densities. We used the Kolmogorov-Smirnov statistics to study both the evolution of the consistency functions and its connection to the evolution of the comoving density of sources. Finally, we fitted the power-law behaviour of the densities along the observer's past lightcone. Results. The analysis of the comoving number density shows that the increased flexibility of the Lemaitre-Tolman-Bondi models is not enough to fit the observed redshift evolution of the number counts, if it is specialised to a recent best-fit giant void parametrisation. The results for the power-law fits of the densities along the observer's past lightcone show general agreement across both cosmological models studied here around a slope of -2.5 +/- 0.1 for the integral number density on the luminosity-distance volumes. The differential number densities show much bigger slope discrepancies Conclusions. We conclude that the differential number densities on the observer's past lightcone were still rendered dependent on the cosmological model by the flux limits of the PEP survey. In addition, we show that an intrinsic evolution of the sources must be assumed to fit the comoving number-density redshift evolution in the giant void parametrisation for the Lemaitre-Tolman-Bondi models used in this work.