Homogeneidades espacial e observacional da distribuição de galáxias - Lemos, Luis Juracy Rangel (2006)
In this work we propose a second way of analysing the homogeneity of the matter distribution in the Universe, called here as observational homogeneity (OH), and which is carried out along the past light cone null type hypersurface. The usual type of homogeneity is given by the Cosmological Principle, called here as spatial homogeneity (SH), and which is defined along space-like hypersurfaces of the spacetime. In this work we adopted the Einstein-de Sitter cosmological model. All discussion regarding homogeneity were done by means of four cosmological distances, namely, the area distance dA, the galaxy area distance dG, the luminosity distance dL and the redshift distance dz. Simulations of various types of counting of cosmological sources were carried out and in the case of an universe model with SH we used the number counting obtained from the Einsteinde Sitter (EdS) model (NEdS), since it assumes the Cosmological Principle. In order to simulate an universe with OH, we adopted the number counts expression advanced by Wertz (1970) and Pietronero (1987) for the galaxy distribution. Starting from two radial density functions defined in Ribeiro (2005), namely the differential density γi and the integral differential density γ ∗ i , we carried out an analysis of spatial and observational homogeneities of the galaxy distribution, were the latter (OH) was defined by the constant value of γ ∗ i . Various plots were presented showing the central role played by the cosmological distance choice. It was also clearly observed that in order to characterize whether or not the large-scale galaxy distribution in the Universe has, or has not, OH, it is necessary to know not only the general mass-energy distribution, which is determined by the count Ni of cosmological sources, but also the geometrical volume which defines the density and, by itself, depends on the cosmological distance.