7 Discussion

As a classical probe, galaxy redshift surveys still remain an important tool for studying cosmology and galaxy formation. On large scales (> 10h− 1 Mpc or so) they nicely complement the cosmic microwave background, supernovae Ia, and gravitational lensing in quantifying in detail the cosmological model. On small scales (< 10h −1 Mpc) the clustering patterns of different galaxy types (defined by structural or spectral properties) provide important constraints on models of biased galaxy formation.

The redshift surveys mainly constrain Ω m via both redshift distortion (which also depends on biasing) and the shape of the Λ-CDM power spectrum, which depends on the primordial spectrum, the product Ωmh, and also the baryon density Ωb. 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 [79Jump To The Next Citation Point] or the SDSS power spectrum [88Jump To The Next Citation Point]. This is illustrated in Table 2 by contrasting the WMAP-alone derived parameters from those derived from WMAP+SDSS [88Jump To The Next Citation Point]. 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 (w = − 1). Within the Λ-CDM model this scenario can be characterised by the six parameters given in Table 2 based on [88Jump To The Next Citation Point]. 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].

Table 2: Derived 6 cosmological parameters from WMAP alone (temperature and polarization) versus WMAP+SDSS (from Tables 2 and 3 of Tegmark et al. [88]). The quoted error bars correspond to 1-σ.
Symbol WMAP alone WMAP+SDSS


Ω Λ 0.75+0.10 −0.10 0.699+0.042 −0.045

Dimensionless cosmological constant

Ω h2 b 0.0245+0.0050 −0.0019 0.0232+0.0013 −0.0010

Baryon density parameter

2 Ωmh +0.020 0.140−0.018 +0.0091 0.1454 −0.0082

Total matter density parameter

σ8 +0.19 0.99−0.14 +0.090 0.917 −0.072

Mass fluctuation amplitude at 8h−1 Mpc sphere (linear theory)

ns 1.02+0.16 −0.06 0.977+0.039 −0.025

Primordial scalar spectral index at −1 k = 0.05 Mpc

τ +0.24 0.21−0.11 +0.083 0.124 −0.057

Re-ionization optical depth

We emphasize that these parameters were fitted assuming the Λ-CDM model. While the degree of such phenomenological successes of the Λ-CDM model is truly amazing, there are many fundamental open questions:

Even if Λ-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.

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