and Cosmology

8.6 Angular Fluctuations of the Cosmic Microwave Background
341
Fig. 8.25. The uppermost curve in each of the two panels
shows the spectrum of primary temperature fluctuations for the
same reference model as used in Fig. 8.24, whereas the other
curves represent the effect of secondary anisotropies. On large
angular scales (small l), the integrated Sachs–Wolfe effect
dominates, whereas the effects of gravitational light deflection
(lensing) and of the Sunyaev–Zeldovich effect (SZ) dominate
at large l. On intermediate angular scales, the scattering of
photons by free electrons which are present in the intergalactic
gas after reionization (curve labeled “suppression”) is the most
efficient secondary process. Other secondary effects which are
included in these plots are considerably smaller than the ones
mentioned above and are thus of little interest here
if Ω b is reduced, since in this case the mean free path of
photons increases, and so the fluctuations are smeared
out over larger scales. Finally, Fig. 8.24(d) demonstrates
the dependence of the temperature fluctuations on the
density parameter Ω m h 2 . Changes in this parameter result
in both a shift in the locations of the Doppler peaks
and in changes of their amplitudes.
From this discussion, it becomes obvious that the
CMB temperature fluctuations can provide an enormous
amount of information about the cosmological
parameters. Thus, from an accurate measurement of
the fluctuation spectrum, very tight constraints on these
parameters can be obtained.
Secondary Anisotropies. In Fig. 8.25, the secondary
effects in the CMB anisotropies are displayed and compared
to the reference model used above. Besides the
already extensively discussed integrated Sachs–Wolfe
effect, the influence of free electrons after reionization
of the Universe has to be mentioned in particular.
Scattering of CMB photons on these electrons essentially
reduces the fluctuation amplitude on all scales,
by a factor e −τ , where τ is the optical depth with respect
to Thomson scattering. The latter depends on the
reionization redshift, since the earlier the Universe was
reionized, the larger τ is. Also visible in Fig. 8.25 is
the fact that, on small angular scales, gravitational light
deflection and the Sunyaev–Zeldovich effect become
dominant. The identification of the latter is possible
by its characteristic frequency dependence, whereas
distinguishing the lens effect from other sources of
anisotropies is not directly possible.
8.6.4 Observations of the Cosmic Microwave
Background Anisotropy
To understand why so much time lies between the
discovery of the CMB in 1965 and the first measurement
of CMB fluctuations in 1992, we note that these
fluctuations have a relative amplitude of ∼ 2 × 10 −5 .
The smallness of this effect means that in order to
observe it very high precisions is required. The main
difficulty with ground-based measurements is emission
by the atmosphere. To avoid this, or at least
to minimize it, satellite experiments or balloon-based
observations are strongly preferred. Hence, it is not surprising
that the COBE satellite was the first to detect
CMB fluctuations. 9 Besides mapping the temperature
distribution on the sphere (see Fig. 1.17) at an angular
resolution of ∼ 7 ◦ , COBE also found that the CMB is
the most perfect blackbody that has ever been measured.
The power spectrum for l 20 measured by
COBE was almost flat, and therefore compatible with
the Harrison–Zeldovich spectrum.
9 With the exception of the dipole anisotropy, caused by the peculiar
velocity of the Sun, which has an amplitude of ∼ 10 −3 ;thiswas
identified earlier