Universality in the Distribution of Caustics in the Expanding Universe

We numerically investigate the long--time evolution of density perturbationsafter the first appearance of caustics in an expanding cosmological model withone--dimensional `single--wave' initial conditions. Focussing on thetime--intervals of caustic appearances and the spatial distribution of causticsat subsequent times, we find that the time--intervals of caustic appearancesapproach a constant, i.e., their time--subsequent ratio converges to 1; it isalso found that the spatial distribution of caustics at a given time featuressome universality rules, e.g., the ratio between the position of the nearestcaustic from the center and that of the second nearest caustic from the centerapproaches a constant. Furthermore we find some rules for the mass distributionfor each caustic. Using these universality constants we are in the position topredict the spatial distribution of caustics at an arbitrary time in order togive an estimate for the power spectral index in the fully--developednon--dissipative turbulent (`virialized') regime.Comment: 23 pages, 19 figure