Generation of Gaussian Density Fields

TL;DR

This paper details analytical and numerical methods for generating Gaussian density fields used in cosmology, including harmonic generation, filtering, and power spectrum normalization, providing a formal reference for researchers.

Contribution

It offers a formal, detailed description of techniques for generating Gaussian density fields, filling a gap in the existing literature for new researchers.

Findings

Provides a comprehensive formal description of density field generation techniques.

Details the normalization of the power spectrum to CMB temperature fluctuations.

Aims to serve as a useful reference for researchers entering the field.

Abstract

This document describes analytical and numerical techniques for the generation of Gaussian density fields, which represent cosmological density perturbations. The mathematical techniques involved in the generation of density harmonics in k-space, the filtering of the density fields, and the normalization of the power spectrum to the measured temperature fluctuations of the Cosmic Microwave Background, are presented in details. These techniques are well-known amongst experts, but the current literature lacks a formal description. I hope that this technical report will prove useful to new researchers moving into this field, sparing them the task of reinventing the wheel.