The ESO Slice Project [ESP] galaxy redshift survey: V. Evidence for a D=3 sample dimensionality

The issue of the approximate isotropy and homogeneity of the observable universe is one of the major topics in modern Cosmology: the common use of the Friedmann-Robertson-Walker [FWR] metric relies on these assumptions. Therefore, results conflicting with the ``canonical'' picture would be of the utmost importance. In a number of recent papers it has been suggested that strong evidence of a fractal distribution with dimension D~2 exists in several samples, including Abell clusters [ACO] and galaxies from the ESO Slice Project redshift survey [ESP].Here we report the results of an independent analysis of the radial density run,N(<R)~R^D, of the ESP and ACO data. For the ESP data the situation is such that the explored volume, albeit reasonably deep, is still influenced by the presence of large structures. Moreover, the depth of the ESP survey (z<0.2) is such to cause noticeable effects according to different choices of k-corrections, and this adds some additional uncertainty in the results. However, we find that for a variety of volume limited samples the dimensionality of the ESP sample is D~3, and the value $D = 2$ is always excluded at the level of at least five (bootstrap) standard deviations. The only way in which we reproduce D~2 is by both unphysically ignoring the galaxy k-correction and using Euclidean rather than FRW cosmological distances. In the cluster case the problems related to the choice of metrics and k-correction are much lessened, and we find that ACO clusters have D_{ACO} = 3.07 +- 0.18 and D_{ACO} = 2.93 +- 0.15 for richness class R \geq 1 and R \geq 0, respectively. Therefore D=2 is excluded with high significance also for the cluster data.