and Cosmology

8. Cosmology III: The Cosmological Parameters
348
The only data point which deviates substantially from
the model is that of the quadrupole, l = 2. In the COBE
measurements, the amplitude of the quadrupole was
also smaller than expected, as can be seen in Fig. 8.29.
If one assigns physical significance to this deviation,
this discrepancy may provide the key to possible extensions
of the standard model of cosmology. Indeed,
shortly after publication of the WMAP results, a number
of papers were published in which an explanation
for the low quadrupole amplitude was sought. Another
kind of explanation may be found in the fact that for the
analysis of the angular spectrum about 20% of the sky
was disregarded, mainly the Galactic disk. The foreground
emission is concentrated towards the disk, and
we cannot rule out the possibility that it has a measurable
impact on those regions of the sphere that have not
been disregarded. This influence would affect the spectrum
mainly at low l. Anomalies in the orientation of
the low-order multipoles have in fact been found in the
data. Currently, there is probably no reason to assume
that the low quadrupole amplitude is of cosmological
relevance. If, on the other hand, future analysis of the
data can rule out a substantial foreground contribution
from the Galaxy (or even from the Solar System), the
low quadrupole amplitude may be a smoking gun for
modifications of the standard model.
Polarization of the CMB. The cosmic background radiation
is blackbody radiation and should therefore be
unpolarized. Nevertheless, polarization measurements
of the CMB have been conducted which revealed a finite
polarization. This effect shall be explained in the
following.
The scattering of photons on free electrons not only
changes the direction of the photons, but also produces
a linear polarization of the scattered radiation. The direction
of this polarization is perpendicular to the plane
spanned by the incoming and the scattered photons.
Consider now a region of space with free electrons. Photons
from this direction have either propagated from
the epoch of recombination to us without experiencing
any scattering, or they have been scattered into our
direction by the free electrons. Through this scattering,
the radiation is, in principle, polarized. Roughly
speaking, photons that have entered this region from
the “right” or the “left” are polarized in north–south direction,
and photons infalling from “above” or “below”
show a polarization in east-west direction after scattering.
If the CMB, as seen from the scattering electrons,
was isotropic, an equal number of photons would enter
from right and left as from above and below, so that
the net polarization would vanish. However, the scattering
electrons see a slightly anisotropic CMB sky, in
much the same way as we observe it; therefore, the
net-polarization will not completely vanish.
This picture implies that the CMB radiation may
be polarized. The degree of polarization depends on
the probability of a CMB photon having been scattered
since recombination, thus on the optical depth with respect
to Thomson scattering. Since the optical depth
depends on the redshift at which the Universe was reionized,
this redshift can be estimated from the degree of
polarization.
In the lower part of Fig. 8.31, the power spectrum
of the correlation between the temperature distribution
and the polarization is plotted. One finds a surprisingly
large value of this cross-power for small l. This measurement
is probably the most unexpected discovery
in the WMAP data from the first year of observation,
because it requires a very early reionization of the Universe,
z ion ∼ 15, hence much earlier than derived from,
e.g., the spectra of QSOs at z 6.
The Future of CMB Measurements. Before discussing
the cosmological parameters that result from
the WMAP data, we will briefly outline the prospects
of CMB measurements in the years after 2005. On the
one hand, WMAP will continue to carry out measurements
for several years, improving the accuracy of the
measurements and, in particular, testing the results from
the first year. The power spectrum of the polarization
itself, to data (February 2006) has not yet been published,
so that we can expect new insights (or another
confirmation of the standard model) from that as well,
in particular regarding the reionization redshift. As for
COBE, the WMAP data will also be a rich source of
research for many years.
Balloon and ground-based observations will conduct
CMB measurements on small angular scales
and so extend the results from WMAP towards
larger l. For example, the experiments DASI, CBI,
and BOOMERANG have measured polarization fluctuations
of the CMB, as well as temperature-polarization
cross-correlations. As their measurements extend to