Chapter 12

Clustering in the universe: from highly

nonlinear structures to homogeneity

Luigi Guzzo

Osservatorio Astronomico di Brera, Italy

12.1 Introduction

This chapter concentrates on a few specific topics concerning the distribution of
galaxies on scales from 0.1 to nearly 1000h−^1 MPc. The main aim is to provide
the reader with the information and tools to familiarize him/her with a few basic
questions:

(1) What are the scaling laws followed by the clustering of luminous objects

over almost four decades of scales?

(2) How do galaxy motions distort the observed maps in redshift space, and how

we can correct and use them to our benefit?

(3) Is the observed clustering of galaxies suggestive of a fractal universe? and

consequently,

(4) Is our faith in the cosmological principle still well placed? i.e. do we see

evidence for a homogeneous distribution of matter on the largest explorable

scales, in terms of the correlation function and power spectrum of the

distribution of luminous objects?

For some of these questions we have a well-defined answer, but for some others
the idea is to indicate the path along which there is still a good deal of exciting
work to be done.

12.2 The clustering of galaxies

I believe most of the students reading this book will be familiar with the beautiful
cone diagramsshowing the distribution of galaxies in what have often been called

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