Spatial and observational homogeneities of the galaxy distribution in standard cosmologies

Context. An important aim of standard relativistic cosmology is the empirical verification of its geometrical concept of homogeneity by considering various definitions of distance and astronomical observations occurring along the past light cone. Aims. We analyze the physical consequences of distinguishing between spatial homogeneity (SH), defined by the Cosmological Principle, and observational homogeneity (OH). We argue that OH is falsifiable by means of astronomical observations, whereas SH can be verified only indirectly. Methods. We simulate observational counts of cosmological sources, such as galaxies, by means of a generalized number-distance expression that can be specialized to produce either the counts of the Einstein-de Sitter (EdS) cosmology, which has SH by construction, or other types of counts, which do, or do not, have OH by construction. Expressions for observational volumes are derived using the various cosmological-distance definitions in the EdS cosmological model. The observational volumes and simulated counts are then used to derive differential densities. We present the behavior of these densities for increasing redshift values. Results. Simulated counts that have OH by construction do not always exhibit SH features. The reverse situation is also true. In addition, simulated counts with no OH features at low redshift begin to show OH characteristics at high redshift. The comoving distance appears to be the only distance definition for which both SH and OH are applicable simultaneously, even though with limitations. Conclusions. We demonstrate that observations indicative of a possible absence of OH do not necessarily falsify the standard Friedmannian cosmology, which implies that this cosmology does not always produce observable homogeneous densities. We conclude that using different cosmological distances in the characterization of the galaxy distribution can produce significant ambiguities in reaching conclusions about the large-scale galaxy distribution in the Universe.