Universality in the distribution of caustics in the expanding Universe

We numerically investigate the long--time evolution of density perturbations after the first appearance of caustics in an expanding cosmological model with one--dimensional `single--wave' initial conditions. Focussing on the time--intervals of caustic appearances and the spatial distribution of caustics at subsequent times, we find that the time--intervals of caustic appearances approach a constant, i.e., their time--subsequent ratio converges to 1; it is also found that the spatial distribution of caustics at a given time features some universality rules, e.g., the ratio between the position of the nearest caustic from the center and that of the second nearest caustic from the center approaches a constant. Furthermore we find some rules for the mass distribution for each caustic. Using these universality constants we are in the position to predict the spatial distribution of caustics at an arbitrary time in order to give an estimate for the power spectral index in the fully--developed non--dissipative turbulent (`virialized') regime.