There are differences in the number of massive clusters ( http://cosmocoffee.info/viewtopic.php?t=1660&highlight= ), the homogeneity scale ( http://cosmocoffee.info/viewtopic.php?t=1543&highlight= ) and the number of superclusters (arXiv:astro-ph/0603764, arXiv:astro-ph/0604539 and arXiv:astro-ph/0605393). In all of these cases, the observations are more homogeneous than expected: there are more large structures, and the scale of statistical homogeneity is larger.

One thing which is sometimes brought up is that in the observations one sees by eye coherent structures which are larger than the estimated homogeneity scale of about 100 Mpc. Of course, in a random realisation there can be such structures by accident, and the issue is how probable they are. That is what this paper sets out to quantify.

The authors analyse the numbers of filaments on the northern and southern part of the 2dF sky and compare to [tex]\Lambda[/tex]CDM simulations. There is an arbitrariness in the definition of a filament, here collapsing to the choice of a linking length for galaxies. It is chosen as 0.69 times the mean intergalactic separation, as this is near the point where the number of filaments reaches a maximum. (It's not clear to me why they don't choose the value where the maximum lies. Also, in figure 2, where both the number of galaxies and its derivative are plotted, the maximum of the function and the zero of its derivative are clearly in different places, which is curious.)

If one the compares simulations populated with semianalytic models and observations, they do not agree. This is ascribed to too many low luminosity galaxies being placed into groups by the semianalytic method. The problem is solved by jettisoning some of those galaxies. The fraction of jettisoned galaxies is determined by looking at the angular distribution of filaments. Due to redshift distortions, there are more filaments in the radial direction, and throwing galaxies away from groups reduces this excess, until the simulations agree with the observed angular distribution. (I don't understand why jettisoning galaxies from groups changes the angular distribution...)

After fixing the angular distribution to agree, the filaments in the simulations and observations are compared. The result is that though they broadly agree, large filaments are rare in the simulations. Of 50 simulations, only one contains a filament that is a large as the largest on in 2dF, and

*none*of the simulations contain two filaments as luminous as the two most luminous ones observed.

The conclusion of the authors is that

*"while this discrepancy could signal a failure of the standard ΛCDM cosmological model on large scales, it seems more plausible that it reflects a shortcoming in the predictions of our models of galaxy formation for the abundance and spatial distribution of galaxies on small scales"*.