The Evolution of Correlation Functions in the Zeldovich Approximation and Its Implications for the Validity of Perturbation Theory

We investigate whether it is possible to study perturbatively the transitionin cosmological clustering between a single streamed flow to a multi streamedflow. We do this by considereing a system whose dynamics is governed by theZel'dovich approximation (ZA) and calculating the evolution of the two pointcorrelation function using two methods: 1.Distribution functions 2.Hydrodynamicequations without pressure and vorticity. The latter method breaks down oncemultistreaming occurs whereas the former does not. We find that the two methodsgive the same results to all orders in a perturbative expansion of the twopoint correlation function. We thus conclude that we cannot study thetransition from a single stream flow to a multi-stream flow in a perturbativeexpansion. We expect this conclusion to hold even if we use the fullgravitational dynamics (GD) instead of ZA. We use ZA to look at the evolutionof the two point correlation function at large spatial separations and we findthat until the onset of multi-streaming the evolution can be described by adiffusion process where the linear evolution at large scales gets modified bythe rearrangement of matter on small scales. We compare these results with thelowest order nonlinear results from GD. We find that the difference is only inthe numerical value of the diffusion coefficient and we interpret thisphysically. We also use ZA to study the induced three point correlationfunction. At the lowest order we find that, as in the case of GD, the threepoint correlation does not necessarily have the hierarchical form. We also findthat at large separations the effect of the higher order terms for the threepoint correlatin function is very similar to that for the the two pointcorrelation and in this case too the evolution can be be described in terms ofComment: 28 pages including 6 figures, Latex, Aastex macros, Accepted in Astrophysical Journa