Introduction to Cosmology

220 Dark Matter

blue galaxies at 1⩽푧⩽ 3 .5, which obviously are very young. There is also evidence

that the galaxy merger rate was higher in the past, increasing roughly as푎−푚or( 1 +푧)푚

with푚≈2–3. All this speaks for a bottom–top scenario.

Large Scale Structure Simulation. The formation and evolution of cosmic struc-

tures is so complex and nonlinear and the number of galaxies considered so enor-

mous that the theoretical approach must make use of either numerical simulations or

semi-analytic modeling. The strategy in both cases is to calculate how density pertur-

bations emerging from the Big Bang turn into visible galaxies. This requires a number

of processes in a phenomenological manner:

(i) the growth of DM haloes by accretion and mergers;
(ii) the dynamics of cooling gas;
(iii) the transformation of cold gas into stars;
(iv) the spectrophotometric evolution of the resulting stellar populations;
(v) the feedback from star formation and evolution on the properties of prestellar
gas;
(vi) the build-up of large galaxies by mergers.
The primary observational information consists of a count of galaxy pairs in the
redshift space coordinates휎, 휋. From this, the correlation function휉(푠)in redshift
space, and subsequently the correlation function휉(푟)in real space, can be evaluated.
Here휉(푠)and휉(푟)are related via the parameter훽in Equation (9.13). From휉(푟),the
power spectrum푃(푘)can in principle be constructed using its definition later, in Equa-
tions (10.8) and (10.9).
The observed count of galaxy pairs is compared with the count estimated from
a randomly generated mass distribution following the same selection function both
on the sky and in redshift. Different theoretical models generate different simula-
tions, depending on the values of a large number of adjustable parameters:ℎ,훺mℎ≡
(훺dmℎ^2 +훺bℎ^2 )∕ℎ,훺b∕훺m,훺 0 ,푛s, the normalization휎 8 and the bias푏between galaxies
and mass.
The CDM paradigm sets well-defined criteria on the real fluctuation spectrum. A
good fit then results in parameter values. Since the parameter combinations here are
not the same as in the CMB analysis, the degeneracy in the 2dFGRS data between
훺mℎand훺b∕훺mcan be removed by combining the CMB and 2dFGRS analyses. Let
us now summarize a few of the results.
If the simulated mass-correlation function휉dm(푟)and the observed galaxy-number
two-point correlation function휉gal(푟)are identical, this implies that light (from galax-
ies) traces mass exactly. If not, they are biased to a degree described by푏.Theresultis
that there is no bias at large scales, as indeed predicted by theory, but on small scales
some anti-bias is observed. This result is a genuine success of the theory because it
does not depend on any parameter adjustments. Independently, weak lensing obser-
vations also show that visible light in clusters does trace mass (all the visible light is
emitted by the stars in galaxies, not by diffuse emission), but it is not clear whether
this is true on galaxy scales.