2ND-ORDER EVOLUTION OF COLD DARK MATTER PERTURBATIONS

Second-order perturbation theory is used to study the non-linear gravitational evolution of the mass distribution on scales of several tens of Mpc in the standard CDM cosmogony. The results show that non-linear evolution can move the first zero-crossing of the matter correlation function outwards if a high normalization is used, but that the change is very small with a more standard 'biased' CDM normalization. If rich clusters occur at the peaks of the primordial perturbation field, then these nonlinear dynamical effects are still negligible compared to the statistical clustering and the increase in zero-crossing scale of ζCdm cannot be expected to alleviate the large-scale structure problem for CDM to any appreciable extent. © Royal Astronomical Society.