Introduction

1 Introduction

Nowadays the exploration of the Universe can be performed by a variety of observational probes and methods over a wide range of the wavelengths: the temperature anisotropy map of the cosmic microwave background (CMB), the Hubble diagrams of nearby galaxies and distant Type Ia supernovae, wide-field photometric and spectroscopic surveys of galaxies, the power spectrum and abundances of galaxy clusters in optical and X-ray bands combined with the radio observation through the Sunyaev–Zel’dovich effect, deep surveys of galaxies in sub-mm, infrared, and optical bands, quasar surveys in radio and optical, strong and weak lensing of distant galaxies and quasars, high-energy cosmic rays, and so on. Undoubtedly gamma-rays, neutrinos, and gravitational radiation will join the above already crowded list.

Among those, optical galaxy redshift surveys are the most classical. Indeed one may phrase that the modern observational cosmology started with a sort of galaxy redshift survey by Edwin Hubble. Still galaxy redshift surveys are of vital importance in cosmology in the 21st century for various reasons:

Redshift surveys have unprecedented quantity and quality:: The numbers of galaxies and quasars in the spectroscopic sample of Two Degree Field (2dF) are $∼$ 250,000 and $∼$ 30,000, and will reach $∼$ 800,000 and 100,000 upon completion of the on-going Sloan Digital Sky Survey (SDSS). These unprecedented numbers of the objects as well as the homogeneous selection criteria enable the precise statistical analysis of their distribution.
The Universe at $z ≈ 1000$ is well specified:: The first-year WMAP (Wilkinson Microwave Anisotropy Probe) data [6 ] among others have established a set of cosmological parameters. This may be taken as the initial condition of the Universe from the point-of-view of the structure evolution toward $z = 0$ . In a sense, the origin of the Universe at $z ≈ 1000$ and the evolution of the Universe after the epoch are now equally important, but they constitute well separable questions that particle and observational cosmologists focus on, respectively.
Gravitational growth of dark matter component is well understood:: In addition, extensive numerical simulations of structure formation in the Universe has significantly advanced our understanding of the gravitational evolution of the dark matter component in the standard gravitational instability picture. In fact, we even have very accurate and useful analytic formulae to describe the evolution deep in its nonlinear regime. Thus we can now directly address the evolution of visible objects from the analysis of their redshift surveys separately from the nonlinear growth of the underlying dark matter gravitational potentials.
Formation and evolution of galaxies:: In the era of precision cosmology among others, the scientific goals of research using galaxy redshift surveys are gradually shifting from inferring a set of values of cosmological parameters using galaxy as their probes to understanding the origin and evolution of galaxy distribution given a set of parameters accurately determined by the other probes like CMB and supernovae.

With the above in mind, we will attempt to summarize what we have learned so far from galaxy redshift surveys, and then describe what will be done with future data. The review is organized as follows. We first present a brief overview of the Friedmann model and gravitational instability theory in Section 2. Then we describe the non-Gaussian nature of density fluctuations generated by the nonlinear gravitational evolution of the primordial Gaussian field in Section 3. Next we discuss the spatial biasing of galaxies relative to the underlying dark matter distribution in Section 4. Our understanding of biasing is still far from complete, and its description is necessarily empirical and very approximate. Nevertheless this is one of the most important ingredients for proper interpretation of galaxy redshift surveys. Section 5 introduces general relativistic effects which become important especially for galaxies at high redshifts. We present the latest results from the two currently largest galaxy redshift surveys, 2dF (Two Degree Field) and SDSS (Sloan Digital Sky Survey), in Section 6. Finally, Section 7 is devoted to a summary of the present knowledge of our Universe and our personal view of the future direction of cosmological researche in the new millennium.