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Super-homogeneity is a property that is supposed to be satisfied by matterfluctuations in all standard theoretical models of structure formation, such asLCDM and its variants. This is a global condition on the correlation propertiesof the matter density field, which can be understood as a consistencyconstraint in the framework of FRW cosmology, and it corresponds to a very finetuned balance between negative and positive correlations of densityfluctuations and to the fastest possible decay of the normalized mass varianceon large scales. By considering several galaxy samples, we discuss that theseare characterized by the presence of large amplitude fluctuations with spatialextension limited only the size of the current samples. There is therefore atension between the standard prediction of super-homogeneity and the detectionof large scale inhomogeneities in the matter distribution at scales of theorder of 100 Mpc/h. We discuss the theoretical implications of these resultswith respect to models of structure formation and to future galaxy and CMBRdata, emphasizing the central role of the super-homogeneity property in thecurrent description of fluctuations in FRW models.

Super-homogeneity and inhomogeneities in the large scale matter distribution