and Cosmology

4. Cosmology I: Homogeneous Isotropic World Models
168
to x ∼ 10 −4 (where essentially all atoms are neutral)
within a relatively small redshift range. The recombination
process is not complete, however. A small
ionization fraction of x ∼ 10 −4 remains since the recombination
rate for small x becomes smaller than the
expansion rate – some nuclei do not find an electron fast
enough before the density of the Universe becomes too
low. From (4.66), the optical depth for Thomson scattering
(scattering of photons by free electrons) can be
computed,
( z ) 14.25
τ(z) = 0.37
, (4.67)
1000
which is virtually independent of cosmological parameters.
Equation (4.67) implies that photons can
propagate from z ∼ 1000 (the last-scattering surface)
until the present day essentially without any interaction
with matter – provided the wavelength is larger
than 1216 Å. For photons of smaller wavelength, the
absorption cross-section of neutral atoms is large. Disregarding
these highly energetic photons here – their
energies are 10 eV, compared to T rec ∼ 0.3 eV, so
they are far out in the Wien tail of the Planck distribution
– we conclude that the photons present in the early
Universe have been able to propagate without further interactions
until the present epoch. Before recombination
they followed a Planck spectrum. As was discussed in
Sect. 4.3.2, the distribution will remain a Planck spectrum
with only its temperature changing. Thus these
photons from the early Universe should still be observable
today, redshifted into the microwave regime of the
electromagnetic spectrum.
Our consideration of the early Universe predicts
thermal radiation from the Big Bang, as was first
realized by George Gamow in 1946 – the cosmic
microwave background. The CMB is therefore
a visible relic of the Big Bang.
The CMB was detected in 1965 by Arno Penzias
& Robert Wilson (see Fig. 4.15), who were awarded
the 1978 Nobel prize in physics for this very important
discovery. At the beginning of the 1990s, the COBE
satellite measured the spectrum of the CMB with a very
high precision – it is the most perfect blackbody ever
Fig. 4.15. The first lines of the article by Penzias & Wilson,
1965, ApJ, 142, 419
measured (see Fig. 4.3). From upper limits of deviations
from the Planck spectrum, very tight limits for possible
later energy injections into the photon gas, and thus on
energetic processes in the Universe, can be obtained. 8
We have only discussed the recombination of hydrogen.
Since helium has a higher ionization energy
it recombines earlier than hydrogen. Although recombination
defines a rather sharp transition, (4.67) tells
us that we receive photons from a recombination layer
of finite thickness (Δz ∼ 60). This aspect will be of
importance later.
The gas in the intergalactic medium at lower redshift
is highly ionized. If this were not the case we would
not be able to observe any UV photons from sources
at high redshift (“Gunn–Peterson test”, see Sect. 8.5.1).
Sources with redshifts z > 6 have been observed, and
we also observe photons with wavelengths shorter than
the Lyα line of these objects. Thus at least at the epoch
corresponding to redshift z ∼ 6, the Universe must have
been nearly fully ionized or else these photons would
have been absorbed by photoionization of neutral hydrogen.
This means that at some time between z ∼ 1000
and z ∼ 6, a reionization of the intergalactic medium
must have occurred, presumably by a first generation
of stars or by the first AGNs. The results from the new
CMB satellite WMAP suggest a reionization at redshift
z ∼ 15; this will be discussed more thoroughly in
Sect. 8.7.
8 For instance, there exists an X-ray background (XRB) which is radiation
that appeared isotropic in early measurements. For a long time,
a possible explanation for this was suggested to be a hot intergalactic
medium with temperature of k B T ∼ 40 keV emitting bremsstrahlung
radiation. But such a hot intergalactic gas would modify the spectrum
of the CMB via the scattering of CMB photons to higher frequencies
by energetic electrons (inverse Compton scattering). This explanation
for the source of the XRB was excluded by the COBE measurements.
From observations by the X-ray satellites ROSAT, Chandra,
and XMM-Newton, with their high angular resolution, we know today
that the XRB is a superposition of radiation from discrete sources,
mostly AGNs.