and Cosmology

1.2 Overview
17
The CMB photons we receive today had their last
physical interaction with matter when the Universe was
about 3.8 × 10 5 years old. Also, the most distant galaxies
and quasars known today (at z ∼ 6.5) are strikingly
young – we see them at a time when the Universe was
less than a tenth of its current age. The exact relation
between the age of the Universe at the time of the light
emission and the redshift depends on the cosmological
parameters H 0 , Ω m ,andΩ Λ . In the special case
that Ω m = 1andΩ Λ = 0, called the Einstein–de Sitter
model, one obtains
t(z) = 2 1
. (1.12)
3H 0 (1 + z)
3/2
In particular, the age of the Universe today (i.e., at z = 0)
is, according to this model,
t 0 = 2 ≈ 6.5 × 10 9 h −1 yr . (1.13)
3H 0
The Einstein–de Sitter (EdS) model is the simplest
world model and we will sometimes use it as a reference,
but recent observations suggest that Ω m < 1and
Ω Λ > 0. The mean density of the Universe in the EdS
model is
ρ 0 = ρ cr ≡ 3H2 0
8πG ≈ 1.9 × 10−29 h 2 gcm −3 , (1.14)
hence it is really, really small.
1.2.7 Structure Formation and Galaxy Evolution
The low amplitude of the CMB anisotropies implies
that the inhomogeneities must have been very small
at the epoch of recombination, whereas today’s Universe
features very large density fluctuations, at least on
scales of clusters of galaxies. Hence, the density field
of the cosmic matter must have evolved. This structure
evolution occurs because of gravitational instability, in
that an overdense region will expand more slowly than
the mean Universe due to its self-gravity. Therefore,
any relative overdensity becomes amplified in time. The
growth of density fluctuations in time will then cause
the formation of large-scale structures, and the gravitational
instability is also responsible for the formation of
galaxies and clusters. Our world model sketched above
predicts the abundance of galaxy clusters as a function
of redshift, which can be compared with the observed
cluster counts. This comparison can then be used to
determine cosmological parameters.
Another essential conclusion from the smallness of
the CMB anisotropies is the existence of dark matter
on cosmic scales. The major fraction of cosmic matter
is dark matter. The baryonic contribution to the matter
density is 20% and to the total energy density 5%.
The energy density of the Universe is dominated by the
vacuum energy.
Unfortunately, the spatial distribution of dark matter
on large scales is not directly observable. We only
observe galaxies or, more precisely, their stars and
gas. One might expect that galaxies would be located
preferentially where the dark matter density is high.
However, it is by no means clear that local fluctuations
of the galaxy number density are strictly proportional
to the density of dark matter. The relation between the
dark and luminous matter distributions is currently only
approximately understood.
Eventually, this relation has to result from a detailed
understanding of galaxy formation and evolution. Locations
with a high density of dark matter can support
the formation of galaxies. Thus we will have to examine
how galaxies form and why there are different kinds of
galaxies. In other words, what decides whether a forming
galaxy will become an elliptical or a spiral? This
question has not been definitively answered yet, but it is
supposed that ellipticals can form only by the merging
of galaxies. Indeed, the standard model of the Universe
predicts that small galaxies will form first; larger galaxies
will be formed later through the ongoing merger of
smaller ones.
The evolution of galaxies can actually be observed
directly. Galaxies at high redshift (i.e., cosmologically
young galaxies) are in general smaller and bluer, and the
star-formation rate was significantly higher in the earlier
Universe than it is today. The change in the mean color
of galaxies as a function of redshift can be understood as
a combination of changes in the star formation processes
and an aging of the stellar population.
1.2.8 Cosmology as a Triumph
of the Human Mind
Cosmology, extragalactic astronomy, and astrophysics
as a whole are a heroic undertaking of the human mind
and a triumph of physics. To understand the Universe we