Discussion

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 [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 ( $w = − 1$ ). Within the $Λ$ -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 ].

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	Description
$Ω Λ$	$0.75+0.10 −0.10$	$0.699+0.042 −0.045$	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:

Both components of the model, $Λ$ and CDM, have not been directly measured. Are they ‘real’ entities or just ‘epicycles’? Historically epicycles were actually quite useful in forcing observers to improve their measurements and theoreticians to think about better models!

‘The Old Cosmological Constant problem’: Why is $ΩΛ$ at present so small relative to what is expected from Early Universe physics?

‘The New Cosmological Constant problem’: Why is $Ω ∼ Ω m Λ$ at the present-epoch? Why is $w ∼ − 1$ ? Do we need to introduce new physics or to invoke the anthropic principle to explain it?

There are still open problems in $Λ$ -CDM on the small scales, e.g., galaxy profiles and satellites.

Could other (yet unknown) models fit the data equally well?

Where does the field go from here? Should the activity focus on refinement of the cosmological parameters within $Λ$ -CDM, or on introducing entirely new paradigms?

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.