Quantifying the evolution of higher order clustering

We use a high-resolution dissipationless simulation to study the evolution of the dark matter and halo distributions in a spatially flat cosmological model dominated by a cosmological constant Λ and cold dark matter (ΛCDM). In order to quantify the evolution of structure, we calculate the Minkowski functionals of the haloes and the dark matter component at various redshifts. A comparison of Minkowski functionals and the more standard correlation function analysis shows that the Minkowski functionals contain information about correlation functions of arbitrary order. While little evolution of the Minkowski functionals of haloes between z=4 and 0 is observed, we find that the Minkowski functionals of the dark matter evolve rapidly with time. The difference of the Minkowski functionals of haloes and dark matter can be interpreted as a scale-dependent bias. This implies that scale-dependent bias is a property not only of the two-point halo correlation function, but also of correlation functions of higher order.