On the Onset of Stochasticity inCDM Cosmological Simulations

The onset of stochasticity is measured inCDM cosmological simulations using a set of clas- sical observables. It is quantified as the local derivative o f the logarithm of the dispersion of a given observable (within a set of different simulations di ffering weakly through their initial realization), with respect to the cosmic growth factor. In a n Eulerian framework, it is shown here that chaos appears at small scales, where dynamic is non-linear, while it vanishes at larger scales, allowing the computation of a critical transition s cale corresponding to � 3.5Mpc/h. This picture is confirmed by Lagrangian measurements which s how that the distribution of substructures within clusters is partially sensitive to in itial conditions, with a critical mass upper bound scaling roughly like the perturbation's amplit ude to the power 0.15. The cor- responding characteristic mass, Mcrit = 210 13 M⊙, is roughly of the order of the critical mass of non linearities at z = 1 and accounts for the decoupling induced by the dark energy triggered acceleration. The sensitivity to detailed initial conditions spills to so me of the overall physical prop- erties of the host halo (spin and velocity dispersion tensor orientation) while other "global" properties are quite robust and show no chaos (mass, spin parameter, connexity and center of mass position). This apparent discrepancy may reflect the fact that quantities which are integrals over particles rapidly average out details of dif ference in orbits, while the other observables are more sensitive to the detailed environment of forming halos and reflect the non-linear scale coupling characterizing the environments of halos.