astro-ph/0103017

# LARGE-SCALE STRUCTURE, THEORY AND STATISTICS

### Peter Coles

School of Physics & Astronomy,
University of
Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

**Abstract.** I review the standard paradigm for understanding the
formation and evolution of cosmic structure, based on the gravitational
instability of dark matter, but many variations on this basic
theme are viable. Despite the great progress that has undoubtedly
been made, steps are difficult because of uncertainties in the
cosmological parameters, in the modelling of relevant physical
processes involved in galaxy formation, and perhaps most
fundamentally in the relationship between galaxies and the
underlying distribution of matter. For the foreseeable future,
therefore, this field will be led by observational developments
allowing model parameters to be tuned and, hopefully, particular
scenarios falsified. In these lectures I focus on two ingredients
in this class of models: (i) the role of galaxy bias in
interpreting clustering data; and (ii) the statistical properties
of the initial fluctuations. In the later case, I discuss some
ideas as to how the standard assumption - that the primordial
density fluctuations constitute a Gaussian random field - can be
tested using measurements galaxy clustering and the cosmic
microwave background.

**Keywords:** cosmology, large-scale structure of the Universe, galaxy
formation

**Table of Contents**

- INTRODUCTION

- COSMOLOGICAL STRUCTURE FORMATION
- Basics of the Big Bang
- Linear Perturbation Theory
- Primordial density fluctuations
- The transfer function
- Beyond linear theory
- Models of structure formation

- OBSERVATIONAL PROSPECTS
- Redshift surveys
- The Galaxy Power-spectrum
- The abundances of objects
- High-redshift clustering
- Higher-order Statistics
- Peculiar Motions
- Gravitational Lensing
- The Cosmic Microwave Background

- TESTING COSMOLOGICAL GAUSSIANITY
- Fourier Description of Cosmological Density Fields
- The Bispectrum and Phase Coupling
- Visualizing and Quantifying Phase Information

- BIAS AND HIERARCHICAL CLUSTERING
- Hierarchical Clustering
- Local Bias
- Halo Bias
- Progress on Biasing

- DISCUSSION

- REFERENCES

For a postscript version of the article, click
here.