UNIVERSALITY OF THE NETWORK AND BUBBLE TOPOLOGY IN COSMOLOGICAL GRAVITATIONAL SIMULATIONS

Using percolation statistics we, for the first time, demonstrate the u niversal character of a network pattern in the real-space, mass distri butions resulting from nonlinear gravitational instability of initial Gaussian fluctuations. Percolation analysis of five stages of the nonl inear evolution of five power-law models [P(k) proportional to k(n) wi th n = +3, +1, 0, -1, and -2 in an Omega = 1 universe] reveals that al l models show a shift toward a network topology if seen with high enou gh resolution. However, quantitatively the shift is significantly diff erent in different models: the smaller the spectral index n, the stron ger the shift. In contrast, the shift toward the bubble topology is ch aracteristic 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 identif y them and corresponds much better to a visual impression. We also fin d that the maximum of the number of structures (connected regions abov e or below a specified density threshold) in the evolved, nonlinear di stributions is always smaller than in Gaussian fields with the same sp ectrum and is determined by the effective slope at the cutoff frequenc y.