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
and
, and will
reach
and
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
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
. In a sense, the origin of the Universe at
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.