Universality of the network and bubble topology in cosmological gravitational simulations

Using percolation statistics we, for the first time, demonstrate the universal character of a network pattern in the real-space, mass distributions resulting from nonlinear gravitational instability of initial Gaussian fluctuations. Percolation analysis of five stages of the nonlinear evolution of five power-law models [P(k) proportional to k(n) with n = +3, +1, 0, -1, and -2 in an Omega = 1 universe] reveals that all models show a shift toward a network topology if seen with high enough resolution. However, quantitatively the shift is significantly different in different models: the smaller the spectral index n, the stronger the shift. In contrast, the shift toward the bubble topology is characteristic only for the n I -1 models. We find that the mean density of the percolating structures in the nonlinear density distributions generally is very different from the density threshold used to identify them and corresponds much better to a visual impression. We also find that the maximum of the number of structures (connected regions above or below a specified density threshold) in the evolved, nonlinear distributions is always smaller than in Gaussian fields with the same spectrum and is determined by the effective slope at the cutoff frequency.