Dark matter clustering in precision cosmology

In this work we study the accuracy of current numerical and analytical models of dark matter evolution and clustering. In the first part, we investigate the impact of setting the initial conditions in N-body dark matter simulations using the standard Zel'dovich approximation. This method produces initial conditions having incorrect second and higher-order density and velocity correlations. This creates transient modes that live long enough to affect the power spectrum, halo mass function and halo correlations in the non-linear regime to a few-percent level at z = 0. These errors are typically larger than the statistical uncertainties in recent mass functions and power spectrum formulae extracted for numerical simulations. We also show how these systematic effects can be significantly reduced by using initial conditions based on second-order Lagrangian perturbation theory.;In the second part of this work, we focus on the generation of vorticity and velocity dispersion. We show that an analytical approach based on the hierarchy of equations that arise from taking moments of the Vlasov equation is not feasible. We tackle the problem by measuring volume-averaged velocity and stress tensor fields from N-body simulations using a Delaunay tessellation method. Then we extend standard cosmological perturbation theory (PT) to estimate the effects of the stress tensor. These corrections set an upper bound to the range of validity of PT, where the corrections become comparable to the density and divergence fields. We show that at z = 0, this breakdown occurs at k ∼ 1 hMpc--1. We also demonstrate that the velocity statistics predicted by renormalized perturbation theory are in agreement with the numerical results obtained from the measured velocity fields.