Are the 2dFGRS superstructures a problem for hierarchical models?

We introduce an objective method to assess the probability of finding extreme events in the distribution of cold dark matter such as voids, overdensities or very high mass haloes. Our approach uses an ensemble of N-body simulations of the hierar- chical clustering of dark matter to find extreme structures. The frequency of extreme events, in our case the cell or smoothing volume with the highest count of cluster-mass dark matter haloes, is well described by a Gumbel distribution. This distribution can then be used to forecast the probability of finding even more extreme events, which would otherwise require a much larger ensemble of simulations to quantify. We use our technique to assess the chance of finding concentrations of massive clusters or super- clusters, like the two found in the two-degree field galaxy redshift survey (2dFGRS), using a counts-in-cells analysis. The Gumbel distribution gives an excellent descrip- tion of the distribution of extreme cell counts across two large ensembles of simulations covering different cosmologies, and also when measuring the clustering in both real and redshift space. We find examples of structures like those found in the 2dFGRS in the simulations. The chance of finding such structures in a volume equal to that of the 2dFGRS is around 2%.