To test the homogeneity of the universe, it should be observed in 3 dimensions on a large scale. On the level of the galaxies, the universe is not at all homogeneous, the galaxies group in cluster (the local cluster in the case of our galaxy) and these clusters group themselves in supercluster. The black matter on which we will return soon agglomerates in the same type of structures.
The observation of the universe on scales larger than made it possible to show than the universe does not comprise any more structures.
They are the great surveys of galaxies SLOAN DIGITAL Sky Survey and 2dF which allowed, while building, the largest sky charts in three dimensions , to show that galaxies, as well as the structures which they form, are distributed in a random way (dodelson2002 & efstathiou2002). Figure 1.2 exit of the survey 2dF shows well the presence of these structures on the small scales, on a large scale, the matter was left again in a random way.
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