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

Abstract

We investigate whether it is possible to study perturbatively the transition in cosmological clustering from a single-streamed flow to a multistreamed flow. We do this by considering a system whose dynamics is governed by the Zeldovich approximation (ZA) and calculating the evolution of the two-point correlation function using two methods, (1) distribution functions and (2) hydrodynamic equations without pressure and vorticity. The latter method breaks down once multistreaming occurs whereas 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 correlation function. We thus conclude that we cannot study the transition from a single-streamed flow to a multistreamed flow in a perturbative expansion. We expect this conclusion to hold even if full gravitational dynamics (GD) is used instead of ZA.