Statistics of extreme objects in the Juropa Hubble Volume simulation

We present the first results from the Juropa Hubble Volume project, based a large N-body, dark matter-only cosmological simulation with a volume of V = (6 h(-1) Gpc)(3), containing 6000(3) particles, performed within the concordance Lambda cold dark matter cosmological model. The simulation volume is sufficient to probe extremely large length-scales in the universe, whilst at the same time the particle count is high enough so that dark matter haloes down to 1.5 x 10(12) h(-1) M-circle dot can be resolved. At z = 0, we identify over 400 million haloes. The cluster mass function is derived using three different halofinders and compared to fitting functions in the literature. The distribution of clusters of maximal mass across redshifts agrees well with predicted masses of extreme objects, and we explicitly confirm that the Poisson distribution is very good at describing the distribution of rare clusters. The Poisson distribution also matches well the level to which cosmic variance can be expected to affect number counts of high-mass clusters. We find that objects like the Bullet cluster exist in the far-tail of the distribution of mergers in terms of relative collisional speed. We also derive the number counts of voids in the simulation box for z = 0, 0.5 and 1.