and Cosmology

8. Cosmology III: The Cosmological Parameters
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From the observed distribution of τ, it is thus possible
to draw conclusions about the distribution of the
gas overdensity ρ g /ρ g . As argued above, the latter
is basically the same as the corresponding overdensity
of dark matter. From an absorption line spectrum,
τ(λ) can be determined (wavelength-)pixel by pixel,
where λ corresponds, according to λ = (1 + z) 1216 Å,
to a distance along the line-of-sight, at least if peculiar
velocities are disregarded. From τ(λ), the overdensity
as a function of this distance follows with (8.22), and
thus a one-dimensional cut through the density fluctuations
is obtained. The correlation properties of this
density are determined by the power spectrum of the
matter distribution, which can be measured in this way.
This probe of the density fluctuations is applied at
redshifts 2 z 4, where, on the one hand, the Lyα forest
is in the optical region of the observed spectrum, and
on the other hand, the forest is not too dense for this analysis
to be feasible. This technique therefore probes the
large-scale structure at significantly earlier epochs than
is the case for the other cosmological probes described
earlier. At such earlier epochs the density fluctuations
are linear down to smaller scales than they are today.
For this reason, the Lyα forest method yields invaluable
information about the power spectrum on smaller
scales than can be probed with, say, galaxy redshift surveys.
We shall come back to the use of this method in
combination with the CMB anisotropies in Sect. 8.7.
8.6 Angular Fluctuations of the Cosmic
Microwave Background
The cosmic microwave background consists of photons
that last interacted with matter at z ∼ 1000. Since the
Universe must have already been inhomogeneous at this
time, in order for the structures present in the Universe
today to be able to form, it is expected that these spatial
inhomogeneities are reflected in a (small) anisotropy of
the CMB: the angular distribution of the CMB temperature
reflects the matter inhomogeneities at the redshift
of decoupling of radiation and matter.
Since the discovery of the CMB in 1965, such
anisotropies have been searched for. Under the assumption
that the matter in the Universe only consists of
baryons, the expectation was that we would find relative
fluctuations in the CMB temperature of ΔT/T ∼ 10 −3
on scales of a few arcminutes. This expectation is based
on the theory of gravitational instability for structure
growth: to account for the density fluctuations observed
today, one needs relative density fluctuations
at z ∼ 1000 of order 10 −3 . Despite increasingly more
sensitive observations, these fluctuations were not detected.
The upper limits resulting from these searches
for anisotropies provided one of the arguments that, in
the mid-1980s, caused the idea of the existence of dark
matter on cosmic scales to increasingly enter the minds
of cosmologists. As we will see soon, in a Universe
which is dominated by dark matter the expected CMB
fluctuations on small angular scales are considerably
smaller than in a purely baryonic Universe. Only with
the COBE satellite were temperature fluctuations in the
CMB finally observed in 1992 (Fig. 1.17). Over the last
few years, sensitive and significant measurements of
the CMB anisotropy have also been carried out using
balloons and ground-based telescopes.
We will first describe the physics of CMB anisotropies,
before turning to the observational results
and their interpretation. As we will see, the CMB
anisotropies depend on nearly all cosmological parameters,
such as Ω m , Ω b , Ω Λ , Ω HDM , H 0 , the
normalization σ 8 , the primordial slope n s , and the shape
parameter Γ of the power spectrum. Therefore, from
an accurate mapping of the angular distribution of the
CMB and by comparison with theoretical expectations,
all these parameters can, in principle, be determined.
8.6.1 Origin of the Anisotropy: Overview
The CMB anisotropies reflect the conditions in the
Universe at the epoch of recombination, thus at
z ∼ 1000. Temperature fluctuations originating at this
time are called primary anisotropies. Later, as the
CMB photons propagate through the Universe, they
may experience a number of distortions along their way
which, again, may change their temperature distribution
on the sky. These effects then lead to secondary
anisotropies.
The most basic mechanisms causing primary
anisotropies are the following:
• Inhomogeneities in the gravitational potential cause
photons which originate in regions of higher den-