THE EVOLUTION OF CORRELATION-FUNCTIONS IN THE ZELDOVICH APPROXIMATIONAND ITS IMPLICATIONS FOR THE VALIDITY OF PERTURBATION-THEORY

We investigate whether it is possible to study perturbatively the tran sition in cosmological clustering from a single-streamed flow to a mul tistreamed how. We do this by considering a system whose dynamics is g overned by the Zeldovich approximation (ZA) and calculating the evolut ion of the two-point correlation function using two methods, (1) distr ibution functions and (2) hydrodynamic equations without pressure and vorticity. The latter method breaks down once multistreaming occurs wh ereas the former does not. We find that the two methods yield the same results to all orders in a perturbative expansion of the two-point co rrelation function. We thus conclude that we cannot study the transiti on from a single-streamed flow to a multistreamed flow in a perturbati ve expansion. We expect this conclusion to hold even if full gravitati onal dynamics (GD) is used instead of ZA. We use ZA to look at the evo lution of the two-point correlation function at large spatial separati ons, and we find that, until the onset of multistreaming, the evolutio n can be described by a diffusion process in which the linear evolutio n at large scales is modified by the rearrangement of matter on small scales. We compare these results with the lowest order nonlinear resul ts from GD. We find that the difference is only in the numerical value of the diffusion coefficient, and we interpret this physically. We al so use ZA to study the induced three-point correlation function. At th e lowest order of nonlinearity, we find that, as in the case of GD, th e three-point correlation does not necessarily have the hierarchical f orm. We also find that at large separations the effect of the higher o rder terms for the three-point correlation function is very similar to that for the two-point correlation, and in this case too the evolutio n can be described in terms of a diffusion process.