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.

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