The fractal distribution of galaxies and the transition to homogeneity

There is an ongoing debate in cosmology about the value of the length scale at which "homogeneity" in the matter distribution is reached or even if su ch a scale exists. In the wake of this debate, we intend in this Letter to clarify the meaning of the statement transition to homogeneity and of the c oncept of correlation length. We show that there are two scales, each assoc iated with the fractal and with the homogeneous regimes of the matter distr ibution, respectively. The distinction between both scales has deep consequ ences, for there can be a regime that, despite having small fluctuations ar ound the average density, exhibits large clusters of galaxies.