The redshift surveys mainly constrain via both redshift distortion (which also depends on
biasing) and the shape of the
-CDM power spectrum, which
depends on the primordial spectrum, the product
, and also the baryon density
. Redshift surveys at a given epoch are not sensitive
to the Dark Energy (or the cosmological constant, in a specific
case), but combined with the CMB they can constrain the cosmic
equation of state.
A good example of the importance of the redshift
surveys in cosmology is given by the recent WMAP analysis of
cosmological parameters, where the estimation of certain parameters
was much improved by adding the 2dF power spectrum of
fluctuations [79] or the SDSS power
spectrum [88
]. This is
illustrated in Table 2 by contrasting the WMAP-alone
derived parameters from those derived from WMAP+SDSS [88
]. Such results are
sensitive to the assumed parameter space and priors, but for
simplicity we quote here the results for the simple six-parameter
model. In this analysis it was assumed that the Universe is flat,
the fluctuations are adiabatic, there are no gravity waves, there
is no running tilt of the spectral index, the neutrino masses are
negligible, and the dark energy is in the form of Einstein’s
cosmological constant (
). Within the
-CDM model this scenario can be characterised by the
six parameters given in Table 2 based on [88
]. The WMAP data used
are both the temperature and polarization fluctuations. It can be
seen that by adding the SDSS information more than halves the
WMAP-only error bars on some of the parameters. These results are
in good agreement with the joint analysis WMAP+2dF [79].
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We emphasize that these parameters were fitted
assuming the -CDM model. While the degree of such
phenomenological successes of the
-CDM model is truly
amazing, there are many fundamental open questions:
Even if -CDM turns out to be the
correct model, it is not yet the “end of cosmology”. Beyond the
‘zero-th order’ task of finding the cosmological parameters of the
FRW model, we would like to understand the non-linear growth of
mass density fluctuations and then the formation and evolution of
luminous objects. The wealth of data of galaxy images and spectra
in the new surveys calls for the development of more detailed
models of galaxy formation. This is important so the comparison of
the measurements (e.g., correlation function per spectral type or
colour) and the models could be done on equal footing, with the
goal of constraining scenarios of galaxy formation. There is also
room for new statistical methods to quantify the ‘cosmic web’ of
filaments, clusters of voids, for effective comparison with the
simulations. It may well be that in the future the cosmological
parameters will be fixed by the CMB, SN Ia, and other probes. Then,
for fixed cosmological parameters, one may use redshift surveys
primarily to study galaxy biasing and evolution with cosmic
epoch.