Path Integral Methods for Primordial Density Perturbations

Abstract

Path integrals may be used to describe the statistical properties of a random field such as the primordial density perturbation field. In this framework the probability distribution is given for a Gaussian random field subjected to constraints such as the presence of a peak of given curvature at a specific location in the initial conditions. An algorithm has been constructed for generating samples of a constrained Gaussian random field on a lattice using Monte Carlo techniques. The algorithm is equivalent to, but much faster than, generating unconstrained random samples repeatedly until a sample is found satisfying the desired constraints to arbitrary precision. The method makes possible a systematic study of the density field around peaks or other constrained regions in the biased galaxy formation scenario and it is effective for generating initial conditions for N-body simulations with rare objects in the computational volume.